Automorphisms of descending mod-p central series

A Note on Absolute Central Automorphisms of Finite $p$-Groups

Let $G$ be a finite group. The automorphism $sigma$ of a group $G$ is said to be an absolute central automorphism, if for all $xin G$, $x^{-1}x^{sigma}in L(G)$, where $L(G)$ be the absolute centre of $G$. In this paper, we study  some properties of absolute central automorphisms of a given finite $p$-group.

On equality of absolute central and class preserving automorphisms of finite $p$-groups

Let $G$ be a finite non-abelian $p$-group and $L(G)$ denotes the absolute center of $G$. Also, let $Aut^{L}(G)$ and $Aut_c(G)$ denote the group of all absolute central and the class preserving automorphisms of $G$, respectively. In this paper, we give a necessary and sufficient condition for $G$ such that $Aut_c(G)=Aut^{L}(G)$. We also characterize all finite non-abelian $p$-groups of order $p^...

RANK p − 1 MOD - p H - SPACES

Different constructions by Cooke, Harper and Zabrodsky and by Cohen and Neisendorfer produce torsion free finite p-local H-spaces of rank l < p−1. The first construction goes through when l = p− 1 and we show the second does as well. However, the space produced need not be an H-space. We give a criterion for when an H-space is obtained. In the special case of rank 2 mod-3 H-spaces, we also give...

Automorphisms of X * 0 (p)

ON ABSOLUTE CENTRAL AUTOMORPHISMS FIXING THE CENTER ELEMENTWISE

Let G be a finite p-group and let Aut_l(G) be the group of absolute central automorphisms of G. In this paper we give necessary and sufficient condition on G such that each absolute central automorphism of G fixes the centre element-wise. Also we classify all groups of orders p^3 and p^4 whose absolute central automorphisms fix the centre element-wise.