Newbetuts

If $(|G|, |H|) > 1$, does it follow that $\operatorname{Aut}(G \times H) \neq \operatorname{Aut}(G) \times \operatorname{Aut}(H)$?

Showing that $ϕ(x)=x^n$ is a homomorphism from $G\to Z(G)$

A finite $p$-group cannot be simple unless it has order $p$

Number of subgroups of prime order

Why isn't there interest in nontrivial, nondiscrete topologies on finite groups?

Dedekind modular law

If $g$ is the generator of a group $G$, order $n$, when is $g^k$ a generator? [duplicate]

References on the theory of $2$-groups.

Rotman's exercise 2.8 "$S_n$ cannot be imbedded in $A_{n+1}$"

Probability that two randomly chosen permutations will generate $S_n$.

Finding all homomorphisms between two groups - couple of questions

How to prove that $\Bbb Z_{p^2}$ is not isomorphic to $\Bbb Z_{p} \oplus\Bbb Z_{p}$ as a $\Bbb Z$-module [duplicate]

A finite group such that every element is conjugate to its square is trivial

Choosing an advanced group theory text: concerns

New posts in finite-groups

Does there exist an $n$ such that all groups of order $n$ are Abelian?

Upper bounds on the size of $\operatorname{Aut}(G)$

Group action conjugation counting argument

Problem from Herstein on group theory

If G is a group of even order, prove it has an element $a \neq e$ satisfying $a^2 = e$. [duplicate]

counting the number of elements in a conjugacy class of $S_n$

If $(|G|, |H|) > 1$, does it follow that $\operatorname{Aut}(G \times H) \neq \operatorname{Aut}(G) \times \operatorname{Aut}(H)$?

Showing that $ϕ(x)=x^n$ is a homomorphism from $G\to Z(G)$

A finite $p$-group cannot be simple unless it has order $p$

Number of subgroups of prime order

Why isn't there interest in nontrivial, nondiscrete topologies on finite groups?

Dedekind modular law

If $g$ is the generator of a group $G$, order $n$, when is $g^k$ a generator? [duplicate]

References on the theory of $2$-groups.

Rotman's exercise 2.8 "$S_n$ cannot be imbedded in $A_{n+1}$"

Probability that two randomly chosen permutations will generate $S_n$.

Finding all homomorphisms between two groups - couple of questions

How to prove that $\Bbb Z_{p^2}$ is not isomorphic to $\Bbb Z_{p} \oplus\Bbb Z_{p}$ as a $\Bbb Z$-module [duplicate]

A finite group such that every element is conjugate to its square is trivial

Choosing an advanced group theory text: concerns