X. Guo
Department of Mathematics, Shanghai University, Shanghai 200444, P.R. China.
[ 1 ] - 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.
[ 2 ] - On finite $X$-decomposable groups for $X={1, 2, 3, 4}$
Let $mathcal {N}_G$ denote the set of all proper normal subgroups of a group $G$ and $A$ be an element of $mathcal {N}_G$. We use the notation $ncc(A)$ to denote the number of distinct $G$-conjugacy classes contained in $A$ and also $mathcal {K}_G$ for the set ${ncc(A) | Ain mathcal {N}_G}$. Let $X$ be a non-empty set of positive integers. A group $G$ is said to be $X$-d...