Intense automorphisms of finite groups
Author(s)
Bibliographic Information
Intense automorphisms of finite groups
（Memoirs of the American Mathematical Society, no. 1341）
American Mathematical Society, c2021
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"September 2021, volume 273, number 1341 (fourth of 5 numbers)"
Includes bibliographical references (p. 115) and index
Description and Table of Contents
Description
Let G be a group. An automorphism of G is called intense if it sends each subgroup of G to a conjugate; the collection of such automorphisms is denoted by Int(G). In the special case in which p is a prime number and G is a finite p-group, one can show that Int(G) is the semidirect product of a normal p-Sylow and a cyclic subgroup of order dividing p?1. In this paper we classify the finite p-groups whose groups of intense automorphisms are not themselves p-groups. It emerges from our investigation that the structure of such groups is almost completely determined by their nilpotency class: for p > 3, they share a quotient, growing with their class, with a uniquely determined infinite 2-generated pro-p group.
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