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I consider the property for a group $G$, that every time you take an element $g$ of prime order in $G$, then there is a complement $H$ to $\langle g\rangle$ in $G$ in the sense that $G=\langle g\rangl …

I recently come across this question: Number of prime factors of the order of a finite non-abelian simple group. What caught my attention is the second question: Does there exist a sequence $\{S_n\}$ …

Are there examples of $p$-groups satisfying the minimal condition on abelian subgroups but do not satisfying the minimal condition on subgroups? Obviously such a group cannot be locally finite. I've …

Let $P$ be an infinite extra special $p$-group for some prime $p$, namely, $Z(P)=P'=\Phi(P)$ and $P/Z(P)$ is infinite elementary abelian. Let $C$ be a Prufer $q$-group for some prime $q\neq p$. Ques …