Abelian subgroups, nilpotent subgroups, and the largest character degree of a finite group

On the norm of the derived‎ subgroups of all subgroups of a finite group

In this paper‎, ‎we give a complete proof of Theorem 4.1(ii) and a new‎ ‎elementary proof of Theorem 4.1(i) in [Li and Shen‎, ‎On the‎ ‎intersection of the normalizers of the derived subgroups of all‎ ‎subgroups of a finite group‎, ‎ J‎. ‎Algebra, ‎323  (2010) 1349--1357]‎. ‎In addition‎, ‎we also give a generalization of Baer's Theorem‎.

Finite $p$-groups and centralizers of non-cyclic abelian subgroups

A $p$-group $G$ is called a $mathcal{CAC}$-$p$-group if $C_G(H)/H$ is ‎cyclic for every non-cyclic abelian subgroup $H$ in $G$ with $Hnleq‎ ‎Z(G)$‎. ‎In this paper‎, ‎we give a complete classification of‎ ‎finite $mathcal{CAC}$-$p$-groups‎.

The Total Number of Subgroups of a Finite Abelian Group

In this note, steps in order to write a formula that gives the total number of subgroups of a finite abelian group are made.

Finite abelian subgroups of the Cremona group of the plane

Finite abelian subgroups of the mapping class group

Let S be a closed, smooth, orientable surface of genus 2. The mapping class group M of S (or MCG) is the group of isotopy classes of homeomorphisms of S . In this paper we shall investigate the conjugacy classes of finite elementary abelian subgroups, and more generally the finite abelian subgroups of M . While the general finite subgroup classification is important we focus on the case where G...