Abstract Definition and 506 Threads

Homework Statement List the elements of the subgroups <3> and <7> in U(20). Homework Equations The Attempt at a Solution U(20)= {1, 3, 7, 9, 11, 13, 17, 19} = <3> = <7>. So basically I have that the common elements of, <3> and <7> and U(20), under + modulo 20, are all...

Homework Statement (a) Suppose a belongs to a group and lal=5. Prove that C(a)=C(a3). (b) Find an element a from some group such that lal=6 and C(a)≠C(a3). Homework Equations The Attempt at a Solution For (a) I know I need to show that every element in the set C(a) is...

Homework Statement For any integer n>2, show that there are at least two elements in U(n) that satisfy x2=1. Homework Equations In my book I found a definition: Define U(n) to be the set of all positive integers less than n and relatively prime to n. The Attempt at a Solution...

Do abstract things (e.g. numbers) and spiritual things exist in addition to physical things? Or is everything physical? I'd say that mathematics is certainly real, yet not physical. It wasn't just invented by humans.

Homework Statement This problem is from Charles C. Pinter's A Book of Abstract Algebra, Second Edition. The problem is B7 of Chapter 2.Show that the operation * is either associative or not. x*y=\frac{xy}{x+y+1} This problem seems simple to me: I keep arriving at YES for an answer...

Hello , I've a question . How Can someone Get Harvard Books on Mathematics generally and Abstract Algebra Specially ? How Can The one Buy it ?

Hey guys, As of now, I am in a sets and logic proof based course (Intro to proof-writing). This course basically teaches logic, how to write proofs using examples of algebraic equations, sets: power sets, unions and intersections of classes, etc. With a C in this course, you can register...

Hello all, In the Fall I am planning on taking Real Analysis, Abstract Algebra and doing an independent study in something(my professor has yet to get back to me on what he is willing to do it in). My question is would it be too much of a workload to try and do another independent study in...

currently i am a math major, still unsure whether pure or applied. i am also looking to double major in physics. which class would be more helpful to me: abstract algebra, or (upper division) ODE class? I have taken the lower division DE class already.

Hello all, I am currently doing a self-study in Abstract Algebra. I was a math major in college (not so long ago), so I have some exposure to upper level math. For one reason or another, I wanted to go back and re-learn Abstract. I was using Fraleigh until I discovered Pinter's text which...

Self Taught Abstract Mathematics Course?? Good evening everyone! I would like to know if anyone has any recommendations for a self-teaching course in abstract mathematics. I have attempted to teach myself abstract algebra and linear algebra but for some reason I cannot find the discipline to...

I need to buy a textbook for self study in abstract algebra for self study. Although I'm a physics major, I have lot's of experience with proof. I'm between Artin's Algebra and Dummit's Abstract Algebra. Which one do you recommend?

How difficult is abstract algebra or group theory, plus complex analysis in relation to calculus?

Homework Statement M = {(pa,b) | a, b are integers and p is prime} Prove that M is a maximal ideal in Z x Z Homework Equations The Attempt at a Solution I know that there are two ways to prove an ideal is maximal: You can show that, in the ring R, whenever J is an ideal such...

First of all, I'd like to say hi to all the peole here on the forum! Now to my question: When reading some general relativity articles, I came upon this strange notation: T^{a}_{b} = C(dt)^{a}(∂_{t})_{b} + D(∂_{t})^{a}(dt)_{b}. Can someone please explain to me what this means? Clearly...

https://www.amazon.com/dp/1111569622/?tag=pfamazon01-20 Any idea?

Homework Statement f is a quadratic function from the second degree and f(a)=bc;f(b)=ac;f(c)=ab Homework Equations Calculate : f(a+b+c) The Attempt at a Solution Can we say that f(a+b+c)=f(a)+f(b)+f(c) and the go on from there plugging in the values of each one are do i have to do...

Help Develop "Tongue in Cheek" Abstract Algebra Proof Hello all, First and foremost I would like to thank everyone on the forum. Your post here have been invaluable in aiding me in completing many of my engineering courses. Now I am attempting to develop a "tongue in cheek" proof using...

Homework Statement Let K \subseteq L be fields. Let f, g \in K[x] and h a gcd of f and g in L[x]. To show: if h is monic then h \in K[x]. The Attempt at a Solution Assume h is monic. Know that: h = xf + yg for some x, y \in K[x]. So the ideal generated by h, (h) in L[x] equals...

Homework Statement Let G be an abelian group of order n. Define phi: G --> G by phi(a) = a^m, where a is in G. Prove that if gcd(m,n) = 1 then phi is an isomorphism Homework Equations phi(a) = a^m, where a is in G gcd(m,n) = 1 The Attempt at a Solution I know since G is an...

hey, I have this group I've been trying to generate using the GenerateGroupoidByRelations[] function but it keeps giving me an error, G = GenerateGroupoidByRelations[{a, b}, {a^4 == e, b^4 == e, a ** b ** a ** b == e, a^3 ** b ** a^3 ** b == e}, SizeLimit -> 60] gives...

Homework Statement Let f be a derivable function at 0 and f'(0)=2 and let a and b in ℝ. Calculate the limit: \lim_{x\rightarrow0}\frac{f(ax)-f(bx)}{x} The Attempt at a Solution I'm not sure but i got 2a-b as my answer but i wan't to know how to solve it the proper way any help is...

Homework Statement Let f: Z to ZxZ be the function defined f(t)=(3t, 3t+1) . Let B denote the subset of ZxZ defined by B={ (5m, 5m+1) : m is an element of Z}. Determine f^-1(B). This means that you should define set S with a property of S=f^-1(B). In addition, your definition of S should make...

Homework Statement If A is a set that contains a finite number of elements, we say A is a finite set. If A is a finite set, we write |A| to denote the number of elements in the set A. We also write |B| < ∞ to indicate that B is a finite set. Denote the sets X and Y by X = {T : T is a proper...

Homework Statement Let p(x)=xx+x+4 Determine a set S such that S ={p(n), n is an element of Z). Your defition of S should not refer to the polynomial p(x). Homework Equations S={n is an element of Z: p(n)=nn+n+4) The Attempt at a Solution I know that we can't take roots of p(x)...

This is not really a homework questions, rather a concept based one. I am studying from Fraleigh's ''Intro to abstract algebra'' and in chapter 15 it states, that for a group G and normal non-trivial subgroup of N of G, the factor group G/N will be smaller than G. I am not sure how he counts the...

A good book on Abstract Algebra that covers major undergraduate and graduate topics? Something rigorous professional and for mathematicians. Not Hungerford please, or any n x $100 book.

Homework Statement Let g_1(t) = t - 1 and g_2(t)= t^2+t. Using the inner product on P_2 defined in example 10(b) with t_1=-1,t_2=0,t_3=1, find a basis for the orthogonal complement of Span(g_1, g_2). Homework Equations From example 10(b) \langle p, q \rangle = \sum_{i=1}^{k+1}...

http://i111.photobucket.com/albums/n149/camarolt4z28/untitled.jpg G/N is the set of all left cosets of N in G. I don't understand the notation. a) The permutations are (1,2), (2,3), (3,1). What are the left cosets - <1>, <2>, <3>? That doesn't make sense with permutations. b) I have...

Homework Statement Let Ts denote the set of points in the x; y plane lying on the square whose vertices are (-s; s), (s; s), (s;-s), (-s;-s), but not interior to the square. For example, T1 consists of the vertices (-1; 1), (1; 1), (1;-1), (-1;-1) and the four line segments joining them...

Let A, B and C be sets. Prove that if A\subseteqB\cupC and A\capB=∅, then A\subseteqC. My attempted solution: Assume A\subseteqB\cupC and A\capB=∅. Then \veex (x\inA\rightarrowx\inB\cupx\inc). I'm not sure where to start and how to prove this. Any help would be greatly appreciated. Thank you.

Homework Statement Let R be a ring and a,b be elements of R. Let m and n be positive integers. Under what conditions is it true that (ab)^n = (a^n)(b^n)? Homework Equations The Attempt at a SolutionWe must show ab = ba. Suppose n = 2. Then (ab)^2 = (ab)(ab) = a(ba)b = a(ab)b = (aa)(bb) =...

Homework Statement The problem says: Suppose that * is an associative binary operation on a set S. Let H= {a ε S l a * x = x * a for all x ε s}. Show that H is closed under *. ( We think of H as consisting of all elements of S that commute with every element in S) My teacher is horrible so...

The problem says: Suppose that * is an associative binary operation on a set S. Let H= {a ε S l a * x = x * a for all x ε s}. Show that H is closed under *. ( We think of H as consisting of all elements of S that commute with every element in S) My teacher is horrible so I am pretty lost in...

Homework Statement Show that the center of a Clifford algebra of order 2^n is of order 1 if n is even, and 2 if n is odd Homework Equations the center of an algebra is the subalgebra that commutes with all elements Clifford algebra of 2^n is defined as being spanned by the bases...

Let G be a non-cyclic group of order pn where p is a prime number. Prove that G has at least p+3 subgroups. Could anyone offer a solution to this problem?

Hi. I've just failed my first test in my Abstract Algebra course... I'm sure I scored a zero. So... needless to say, I need help. Do you know of any good websites with lots of examples? Or even a really good book with lots of problems? The textbook we're using is 'A First Course in Abstract...

(1)Assume a, b and n are nonzero integers. Prove that n is divisible by ab if and only if n is divisible by a and n is divisible by b.I'm wrong and can't remember why. I spoke to the professor about it for ~ 1 minute so it seems to have slipped my mind, it was because in one case it's true and...

Wave function is always in abstract space in any quantum interpretation be it Copenhagen or Bohmian or Many Worlds because wave function is in many dimensional abstract Hilbert Space. Correct? Since the counterpart of Hilbert space in QM is Fock Space in QFT. Then the fields in QFT live in...

So, my problem statement is: Suppose that two operators P and Q satisfy the commutation relation [Q,P] = Q . Suppose that ψ is an eigenfunction of the operator P with eigenvalue p. Show that Qψ is also an eigenfunction of P, and find its eigenvalue. This shouldn't be too difficult, but...

Show that \langle a,b \rangle = \langle a,ab \rangle = \langle a^-1,b^-1 \rangle for all a and b in a group GI am not sure what this question is asking. Does this notation mean that a the cyclic group is generated by a,b and any combination of the two?

1. There should be a separate (sub)forum for NT. ... and one for abstract algebra, for that matter! 2. Show that there are infinitely many n such that both 6n + 1 and 6n - 1 are composite. Without CRT, if possible. My work... let n = 6^{2k}. Then 6n \pm 1 = 6^{2k + 1} \pm 1... Hmm. Having a...

Homework Statement a.) Let a=3-8i and b=2+3i. Find x,y ϵ Z[i] such that ax+by=1. b.) Show explicitly that the ideal I=(85,1+13i) \subseteq Z[i] is principle by exhibiting a generator. Homework Equations Given ideal: I=(85,1+13i) \subseteq Z[i] a=3-8i b=2+3i Honestly, I am beyond lost...

Homework Statement Let a=p_{1}^{r_{1}}p_{2}^{r_{2}}...p_{k}^{r_{k}}, b=p_{1}^{s_{1}}p_{2}^{s_{2}}...p_{k}^{s_{k}} where p_{1},p_{2},...,p_{k} are distinct positive primes and each r_{i},s_{i} ≥ 0 Prove that (a,b)=p_{1}^{n_{1}}p_{2}^{n_{2}}...p_{k}^{n_{k}} \mbox{ where for each } i...

Homework Statement How do I determine the parity of a permutation? I think my reasoning may be faulty. By a theorem, an n-cycle is the product of (n-1) transpositions. For example, a 5 cycle can be written as 4 transpositions. Now say I have a permutation written in cycle notation: (1...

I'm an undergrad math major, and this is my first semester taking upper level math. I'm currently taking Abstract Algebra, and feeling pretty intimidated. I mean, I feel out of the loop, I'm trying hard to understand, but I feel overwhelmed, like maybe it's too much for me. Is it normal to feel...

Hi, I'm doing a Physics undergrad and this semester I have the following courses: Thermodynamics, Quantum Mechanics, Numerical Methods, an Astrophysics course, and a Computational Lab. I've also taken Abstract Algebra which has twice as many lectures as any of these. Add to this the fact that I...

Homework Statement (E) is a group of points M from a level/plane MA^{2}-MB^{2}=-4 And I is the center of [AB] Homework Equations show that IM*AB=-2 ( IM and AB have arrows on top) The Attempt at a Solution Well i split MA^{2}-MB^{2}=(MA-MB)(MA+MB) then i got ...

Write the following in two row matrix form. (1874)(36759) I have [1 2 3 4 5 6 7 8 9] [8 2 6 1 9 7 4 7 3] my problem is couldn't 7 also go to 5 and have 8 going to 7 and 6 going to 7 so I am sure I am wrong but I am not sure why.

Does anyone here know any good websites or sources to help me learn and understand abstract ablegra?