Group theory Definition and 365 Threads

Question 1 a Find the order of (\mathbb{Z}_4 \times \mathbb{Z}_2) \backslash \langle (2,1) \rangle. Question 1 b Find the order of (\mathbb{Z}_2 \times \mathbb{Z}_4) \backslash \langle (1,1) \rangle.

I need some help on solving these sorts of problems in Group theory. Question Consider the group action of S_4 on itself by conjugation. Determine the orbit and the stabilizer of x = (12)(34)

Let H be a finite-indexed infinite subgroup of an infinite group G. Suppose: G = \bigcup _{i = 1} ^{k} g_i H then J = \bigcap _{i = 1} ^{k} g_i H g_i ^{-1} is a normal subgroup of G and an intersection of all of the (finitely many) conjugates of H. Show that J has a finite index.

Problem 1 \alpha ,\, \beta \in S_n,\ \alpha \beta = \beta \alpha and \alpha is an n-cycle. Prove that \beta is a power of \alpha. I know that either \beta = \epsilon, or \beta permutes all the elements, but I don't know how to prove that it must specifically be a power of \alpha. Problem...

I'm trying to get a handle on the rotation group in quantum mechanics. Does anyone have suggestions or links to clear and consise statements of this material. I am looking for a level of about Sakurai. Thanks

seeing lots of group theory here after a really long time... let G be a finite group of order n, where n is not divisible by 3. suppose (ab)^3 = a^3 b^3 ,for a, b in G . prove that G is abelian.

i've just started out with a course in group theory...here's a question that's been bothering me for a while now... let G be a group and 'a' ,a unique element of order 2 in G. show that a belongs to Z(G). if every element of the group has order 2 this is pretty easy...but that's not the case...

I lost my notes for the Intro to Group Theory part of my algebra course last year, and need to know a coulple definitions before i go back to uni this year: ORDER of a group, and CYCLIC group. Thanks Ray Veldkamp

I'd like to learn group theory to understand QM and particle theory, and I looked at several books on discrete mathematics but they didn't mention SU groups. I'm an absolute beginner in group theory or discrete math, but I don't want to spend too much time on materials unrelated to physics. Do...

What does it mean to say that a n x n orthogonal matrix has n(n-1)/2 independent parameters? And why is this so? Can this be shown using the equation the summation with respect to i of the product aij(aik)= bjk where j,k=1,2,3. And bjk has the property bjk=1 when j=k...

I'm looking for a good introduction on quantum group theory for someone who has already had a semester class on group theory. I'll be putting together a short paper (5 pages) on the topic with the intended audience of college math majors. My naive understanding is that symmetry and interaction...

I'm currently making my way through "Groups and Symmetry", by M. A. Armstrong [ISBN 0387966757], and I'm stuck on what seems like it should be a very simple exercise. Page 14, problem 3.8, states: However, I can't make this work unless I change the "or" to an "and". So, is this a misprint...

In trying to get my head round GR and quantum gravity, I'm puzzled about the following questions: Is the gauge group for gravity defined as the set of all possible Weyl tensors on a general 4D Riemann manifold? Which abstract group maps onto this set? Is it GL(4) or a subgroup of GL(4)? How...

Group Theory: Find the order of ... Hello, This is a question I have been given for homework. I would post this in homework section of the forum, but I need more than help to find a solution - I want to understand it. Explanation and understanding it is much more important to me than whether...

[SOLVED] Group Theory For Dummies I've become interested in learning about Group Theory. I don't know too much but I see it spring up all over the place and would just like to know what it is about and some of the basics. Could some one please point me in the direction of a good resource that...