On Class-Preserving Coleman Automorphisms of Finite Separable Groups

Abstract

Let G be a finite separable group. It is shown that under some conditions class-preserving Coleman automorphisms of 2-power order of G are inner. Interest in such automorphisms arose from the study of the normalizer problem for integral group rings. Our theorems generalize some well-known results.

Coleman automorphisms of finite groups with a self-centralizing normal subgroup

“…Petit Lobão and Sehgal in [16] showed that the normalizer property holds for the wreath product G = N wrS m of a finite nilpotent group N by symmetric group S m . In addition, other affirmative results concerning this problem can also be found in [1], [2], [3], [4], [7], [11], [12], [13], [14], [15].…”

Coleman Automorphisms of Some Metabelian Groups

“…In [2], Krempa proved that Out Z (F) is a 2-group. us, if we show that Out Col (F) is a group of odd order or Aut Col (F) Inn(F) under some conditions, then Aut Z (F) Inn(F), that is, the normalizer problem holds for F. Related results on this subject can be found in [3][4][5][6][7][8][9]. e purpose of this study is to determine the structure of the Coleman automorphism groups of some metabelian groups.…”