Suzuki $2$-groups

Abstract

1. Introduction In this paper we shall determine all groups G of order a power of 2 which possess automorphisms that permute their involutions cyclically. The de- termination is complete, except that we do not exclude the possibility that two or more of the groups that we list may be isomorphic. The investigation is perhaps not without interest simply as an example of the use of linear methods in p-group theory; but the main motivation for it is that some result along these lines is needed by Suzuki in his classification [4] of ZT-groups. It is a pleasure to acknowledge that this paper is, in a direct way, a fruit of the special year in Group Theory organized by the Department of Mathematics at the University of Chicago.