New posts in finite-groups

Does $A^{-1}A=G$ imply that $AA^{-1}=G$? [closed]

Qualifying Exam Question On Elementary Group Theory

Finite abelian group contains an element with order equal to the lcm of the orders of its elements

What is this method called - Abelization of a Group.

Finite group is abelian if the representatives of its conjugacy classes commute

A conjugacy class $C$ is rational iff $c^n\in C$ whenever $c\in C$ and $n$ is coprime to $|c|$.

Which families of groups have interesting formulas for the number of elements of given order?

Decomposition of Permutation Representation

Uniqueness of the direct product decomposition of finite groups

Cancellation of Direct Product in Grp

Prove that a group with exactly two proper nontrivial subgroups is isomorphic to $\mathbb{Z}_{pq}$ or $\mathbb{Z}_{p^3}$.

An abelian subgroup of symmetric group

How can I compute $\mathrm{Aut}(\mathbb{Z}/4\mathbb{Z}\times\mathbb{Z}/6\mathbb{Z})$?

Examples of finite groups that are not a semidirect product

Left and right transversals of groups.

Calculating the group co-homology of the symmetric group $S_3$ with integer coefficients.

Finite groups of which the centralizer of each element is normal.

Show that if $|G|=30$ then $G$ has normal $3$-Sylow and $5$-Sylow

Group of order $105$ has a subgroup of order $21$

Only a solvable group can have 3 Sylow p-subgroups