New posts in finite-groups

(finitely generated finite by abelian) implies (abelian by finite)

After using Sylow Theorems, how can we say how many elements of order 5 might be there in a group of order 20? [duplicate]

$G$ simple group and there exists a subgroup of index $n$. Show that: $|G|$ divides $n!/2$

Isomorphism between $U_{10}$ , $U_8$ , $U_5$

Is there something wrong with this question concerning Groups

Conjugates and commutators for twisty puzzles -- so what?

Ordering finite groups by sum of order of elements

non-capable groups and their direct products

Applying Burnside's Lemma to a Permutational Problem.

Endomorphism algebra of irreducible module over a group algebra

A question about finite group acting on inputs and outputs of maps between vector spaces.

Quaternion Group as Permutation Group

If a finite group $G$ of order $n$ has at most one subgroup of each order $d\mid n$, then $G$ is cyclic

Let $G$ be a finite Abelian group that has exactly one subgroup for each divisor of $|G|$. How does this imply that $G$ is cyclic? [duplicate]

Platonic Solids

Let $\phi:\Bbb{Z}_{20} \to \Bbb{Z}_{20}$ be an automorphism and $\phi(5)=5$. What are the possibilities of $\phi(x)$?

Rotman introduction to theory of groups exercise

Groups where no elements commute except for the trivial cases

Let $a$ be an element of order $n$ in a group $G$. If $a^m$ has order $n$, then $m$ and $n$ are relatively prime.

Metric on a group