Abstract Definition and 506 Threads

I'm supposed to find a non-trivial group G such that G is isomorphic to G x G. I know G must be infinite, since if G had order n, then G x G would have order n^2. So, after some thought, I came up with the following. Z is isomorphic to Z x Z. My reasoning is similar to the oft-seen proof...

Can someones tells me how to prove these theorems. 1. Prove that if G is a group of order p^2 (p is a prime) and G is not cyclic, then a^p = e (identity element) for each a E(belongs to) G. 2. Prove that if H is a subgroup of G, [G:H]=2, a, b E G, a not E H and b not E H, then ab E H. 3...

Given R=all non-zero real numbers. I have a mapping Q: R-> R defined by Q(a) = a^4 for a in R. I have to show that Q is a homomorphism from (R, .) to itself and then find kernel of Q. In order to prove homomorphism i did this, for all a, b in R Q(ab) = (ab)^4 = a^4b^4 = Q(a)Q(b). Is...

1) prove that H is a subgroup of S5 (the permutation group of 5 elements). every element x in H is of the form x(1)=1 and x(3)=3, meaning x moves 1 to 1 and moves 3 to 3. does your argument work hen 5 is replaced by a number greater than or equal to 3? 2) Let G be a group. prove or disprove...

Hi. My latest question concerns the following. I must prove that the alternating group A_n contains a subgroup that is isomorphic to the symmetric group S_{n-2} for n = 3, 4, ... So far, here's what I have (not much). The cases for n = 3 and n = 4 are elementary, since the group lattices...

Abstract algebra help please! I'm not sure if I've posted in the correct forum but I would like some help with the following question: http://i12.tinypic.com/33mlik6.jpg" I've to complete this table but I am unsure of how to do the very first step which is to fnd wv. I am learning this...

Hi I'm fairly new at abstract algebra and have therefore got stuck with this assignment. Hope there is somebody here who can help me complete it, because I have been ill these last couple of weeks. Its goes something like this b is a number written in base 10 b\;= \;b_010^0 +...

I have finally understood algebra. It is all about understanding groups. first of all we tackle abelian groups, and finitely generated ones at that., we completely classify them as sums of cyclic groups using their structure as Z modules where Z is the integers. then we ask about non...

It roughly says there exists a continuous function from a normal space X to some interval [a,b] Since the the space is a normal space, there exist two disjoints closed subsets A and B. What I don't understand is how can you associate some abstract space with a real interval and is...

This is question 53\gamma. Given a group G of transformations that acts on X... and a subgroup of G, Go (g * x = x for all x for each g in Go), show that the quotient group G/Go acts effectively on X. A group G "acts effectively" on X, if g * x = x for all x implies that g = e, where g is a...

hello i have two questions and i need answers for them first one: in the additive group (Z,+) show that nZ intersection mZ= lZ , where l is the least common multiple of m and n. The second question is : Given H and K two subgroups of a group G , show the following...

I decided to group my threads into one, as I'm finding more and more problems that I need help on. I hope I haven't hurt anyone by doing so. PROBLEMS I NEED HELP WITH: 1) find an integral domain where NOT every element (not a unit) is expressible as a finite product of irreducibles...

Lately I've been taking a unit that deals with abstract algebra and I'm finding myself not understanding the lectures at all. To make matters worse the unit doesn't have a reccomended textbook so I don't even have any infomation to self learn from. I guess what I'm asking is for some good...

Hi everyone; There are some questions which are frizzling my mind, if anybody could help then please reply to these ques which are as follows. Q1) Prove that homomorphic image of cyclic group is itself cyclic? Q2) Prove that any group 'G' can be embedded in a group of bijective mapping of...

What should I expect out of a course named Abstract Linear Algebra? I have just taken two courses on Linear Algebra, and it was mainly computational. I was hoping that this course would not involve any computations, but the professor says we will have some (how much?) on our next midterm...

i reackon youv'e seen it already, the problem is to rearrange the next numbers in the fixed order: 1 2 3 4 5 6 7 8 9 11 10 when you have at the last entry a vacant place you need to put it in order. this is from the text of edwin h. connell, and i think it's impossible (after a lot...

Hello, everyone, i am a newbie here. I am currently taking a modern linear algebra course that also focus on vector spaces over the fields of Z[SIZE="1"]p and complex numbers. Since i am not familiar with typing up mathematics using tex or anything so that i can post on the forums, i will use...

I just started with the course of discrete mathematics,,where we have abstract algebra..I am actually interested in the application of this algebra..i know that this is used in Cryptography,error correcting codes,and theoritical computer science...i just want to have a basic outline of how they...

always abstract? things are really very abstract in algebra as its name.But it would be nicer to learn some applications especially to physics apperently there are applications about groups but i could not find anything related to rings ideals etc. discussing the applications would make...

Does anyone know a good Abstract Algebra text? I currently have the text by Gallian and quite frankly I give two stars out of five. I'm looking for something that's more advanced, and well written. Any recommendations will be greatly appreciated. :biggrin:

Let R be the set of all real valued functions defined for all reals under function addition and multiplication. Determine all zero divisors of R. A zero divisor is a non zero element such that when multiplied with another nonzero element the product is zero. So I said that the zero...

Hello. We got a review today in abstract algebra, and I am stuck on two problems. 1) Let f: G -> H be a surjective homomorphism of groups. Prove that if K is a normal subgroup of G, then f(K) is a normal subgroup of H. Where f(K)= {f(k): k \inK} The entire f(K) part is really throwing me...

I'm 17 and my high school has no other math courses to offer me. At a local college there is a course called "Modern Algebra" and I was wondering if it was the same thing as abstract algebra. I asked my math teacher about it, and he said it was the hardest math class he took; he used to call...

Help with abstract algebra! Here is my quetion. What is the order of the set of all 2x2 matricies (such that its entries a,b,c,d are between 0 and p-1), and whose determinant is congruent to 1 modulo p ? => Order of SL(2,Fp) thanks :)

Hello. I was reading a journal and an interesting problem came up. I believe the journal was in the American Mathematics Society publications. Well, here's the statement. "For all integers, n greater than or equal to 3, the number of compositions of n into relatively prime parts is a...

define right-inverse of a mapping B to be mapping A, such that B * A= identity (iota). Where the operation * is composition. Note that B is A's left-inverse. QUESTION: Assume S is a nonempty set and that A is an element of M(S) -the set of all mappings S->S. a) Prove A has a left...

physics, abstract... i am very confused about what the following abstract says: The main purposes of this paper are (i) to illustrate explicitly by a number of examples the gauge functions chi(x, t) whose spatial and temporal derivatives transform one set of electromagnetic potentials into...

This coming fall semester, I have a choice between taking Analysis and Abstract Algebra. Unfortunatly, I'm having a great deal of trouble deciding which to take. Both seem interesting (though Algebra more so). On the other hand, Analysis would open more options for spring semester (in...

Abstract: hbar=e^2/e0c hbar=[1.6021765(31) x 10^-19 A-s]^2/[8.854187817... x 10^-12 A^2-s^4/kg-m^3-sr][2.99792458 x 10^8 m/s] hbar=[2.5669696(36) x 10^-38 A^2-s^2]/[2.6544187(29) x 10^-3 A^2-s^3/kg-m^2-sr] hbar=[9.6705527(59) x 10^-36 kg-m^2-sr/s] Introduction: Planck constant: h =...

I need some recommendations for a good linear algebra textbook, something that's actually used in schools. I've finished linear 1 and 2 and I'm doing some preparation during the summer.

Here is one of my pictures. I make these in Paint. I chose this one because it's pretty good, but not so good I'd feel funny about sharing it. If you just don't like abstract art then don't look at it.

This and your other posts here are good info. Thanks.

I was given a problem to prove there are at most 3 groups of order 21, with extra credit for proving there are at most 2. I am pretty stuck on this one but here is what I have so far: Suppose G is a group of order 21 Let K be a sylow 3-subgroup of G and let H be a sylow 7-subgroup of G...

My prof. assigned this problem as the only one for HW a few days back, and for some reason the answer seems too obvious. What subtleties could I possibly be missing? Let G be a group of permutations in a set S. If x, y \in S and y \in orb_g(x), then orb_g(y) = orb_g(x) Still, I am...

Question 1 Determine the quotient group (\mathbb{Z}_2\times\mathbb{Z}_4)/\langle(1,2)\rangle Answer \langle(1,2)\rangle is a cyclic subgroup H of \mathbb{Z}_2\times\mathbb{Z}_4 generated by (1,2). Thus H=\{(0,0),(1,2)\} Since \mathbb{Z}_2\times\mathbb{Z}_4 has 2.4 = 8 elements, and...

Salutations everyone, Thank you everyone in this community for taking the time to read my message. I am a third grade teacher in Moreno Valley, California USA. It is my conjecture as a third grade teacher that the encoding during reading in constructing meaning from words is similar to the...

I was given this problem to work out but I'm still a little bad when it comes to proofs, but here's the question. I have given it a little thought but I can't seem to prove what I feel is the correct answer without brute forcing the answer in such an ugly way. Let G = S_7, where S_7 is the...

This should probably be posted in the math forums but I guess it would fall under here because it's a HW question due late tomorrow. If G is a group, prove that Aut(G) and Inn(G) are groups, where Aut(G) is the set of automorphisms of G and Inn(G) is the set of inner automorphisms of G For...

Hello, I am a student at CMU, enrolled in the Abstract Algebra class. I'm having trouble with a few problems, see if you can figure them out. Show that for every subgroup $J$ of $S_n|n\geq 2$, where $S$ is the symmetric group, either all or exactly half of the permutations in $J$ are...

I Do a web search on 'abstract art' and browse around at the paintings... It's a great way to get a feel for the word 'abstract'. It's easy to know a definition, it is harder to gain experience of a concept. When i look at a variety of paintings and really 'understand' what the word abstract...

what is the abstract reasoning and how to use it?

Pretty straightforward, right? I want some definitions for "abstract" and "concrete". If anyone is interested in doing some reading, here are some links: 1, 2, 3, 4, 5(PDF), http://64.233.187.104/search?q=cache:AUWz3yToePIJ:www.hcrc.ed.ac.uk/cogsci2001/pdf-files/1106.pdf . I see a connection...

I'm having trouble finding any good books and sites from which i can learn abstract algebra. Does anyone have any good suggestions so that i can learn the course? please include prices if possible

Hello all I know an interface is even more abstract then an abstract class. Let's say I want to make an interface called Furniture that implements two class called Chair and Table. What does this exactly mean? Can someone please clarify this? Thanks public interface Furniture { int...

let G be a non-trivial group whose only supgroups are {e} and G. Show that G is cyclic of prime order. ok...so basically, it is asking I need show that it is cyclic that has an order that is only divisible by 1 and itself right? I don't know how to approace this, but I know the...

My question is regarding abstract algebra. Suppost that B is a 10-cycle. For which integers i between 2 and 10 is B^(i) also a 10-cycle? I know that the answer is 3, 7, and 9 I just don't know how you arrive at these numbers. If...

Hi ppl, Could someone please tell me who's quote this is: "Mathematics is the purest form of abstract thought"?

i have a question about elements in SL(2,Z3), a,b,c,d are intergers and ad-bc=1 or Det [A]=1. i have to write all the matrices of this group and prove that I do have all of them. i know that only 3 elements exists in Z3 {[0],[1],[2]} with all others just being repeats. i.e. [-3]=0, [[4]=[1]...

Frustrating step in a proof -- basic abstract algebra Hello all, I am trying to work on a proof related to information theory, and I have gotten stuck. I am nearly 100% this is true, but it might not be . . . and I am having trouble coming up with a proo for it in any case! ---------- M...

Hello all. I'm currently putting together a book called Encyclopedia of Abstract Terms. I was wondering if you could provide me with abstract words from philosophy that you believe need (better) definition.