Groups with all elements of finite length

Maximal Length Elements of Excess Zero in Finite Coxeter Groups

Finite groups all of whose proper centralizers are cyclic

‎A finite group $G$ is called a $CC$-group ($Gin CC$) if the centralizer of each noncentral element of $G$ is cyclic‎. ‎In this article we determine all finite $CC$-groups.

Pairwise‎ ‎non-commuting elements in finite metacyclic $2$-groups and some finite $p$-groups

Let $G$ be a finite group‎. ‎A subset $X$ of $G$ is a set of pairwise non-commuting elements‎ ‎if any two distinct elements of $X$ do not commute‎. ‎In this paper‎ ‎we determine the maximum size of these subsets in any finite‎ ‎non-abelian metacyclic $2$-group and in any finite non-abelian $p$-group with an abelian maximal subgroup‎.

Finite Groups With a Certain Number of Elements Pairwise Generating a Non-Nilpotent Subgroup

Elements with Square Roots in Finite Groups

In this paper, we study the probability that a randomly chosen element in a finite group has a square root, in particular the simple groups of Lie type of rank 1, the sporadic finite simple groups and the alternating groups.