New posts in Finite Groups

Elements in a finite group of order prime

Exercise 6.11 from Isaac's Character theory of finite groups.

When does the product of all elements in a finite abelian group equal $1$?

Showing $b^2 \notin \langle a \rangle$ for $V_{8n}=\langle a,b:a^{2n}=e, b^4 = e, ba=a^{-1}b^{-1},b^{-1}a=a^{-1}b\rangle.$

Does one of the orthogonal groups $O^\pm(2n,2)$ always have an element of order $2n+1$

Groups of order $p^3$

Does a group of order $400$ always have a subgroup of order $200$?

$G$ is a finite group s.t. $(ab)^p=a^pb^p$; $P$ is its $p$-Sylow subgroup. Then there exists $N \unlhd G$ such that $N \cap P = (e)$ and $NP=G$.

Groups where no elements commute except for the trivial cases

Does $A_{17}$ have a subgroup of index $3$?