Abstract algebra Definition and 459 Threads

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...

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'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

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...

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...

I downloaded that book from the physics Napster. It looks like something I should be able to handle, but I need help understanding some of the notation. "Any set called an index set is assumed to be non-void. Suppose T is an index set and for each t within T, At is a set. [inter] At =...