Class-preserving coleman automorphisms of permutational wreath products with 2-closed base groups-Reference-Cited by-同舟云学术

Class-preserving coleman automorphisms of permutational wreath products with 2-closed base groups

Published:2016-11-24 Issue:10 Volume:15 Page:1650189
ISSN:0219-4988
Container-title:Journal of Algebra and Its Applications
language:en
Short-container-title:J. Algebra Appl.

Author:

Li Zhengxing¹²,Li Yuanlin³

Affiliation:

1. College of Mathematics, Qingdao University, Qingdao, Shandong 266071, P. R. China

2. College of Automation Engineering, Qingdao University, Qingdao, Shandong 266071, P. R. China

3. Department of Mathematics and Statistics, Brock University, St. Catharines, Ontario, L2S 3A1, Canada

Abstract

Let [Formula: see text] be a nontrivial [Formula: see text]-closed group and let [Formula: see text] be an arbitrary permutation group on a finite set [Formula: see text]. Let [Formula: see text] be the corresponding permutational wreath product of [Formula: see text] by [Formula: see text]. It is shown that every class-preserving Coleman automorphism of [Formula: see text]-power order of [Formula: see text] is inner. As a direct consequence, it is obtained that the normalizer property holds for [Formula: see text]. Further, it is shown that every class-preserving Coleman automorphism of [Formula: see text] is inner whenever [Formula: see text] is nilpotent. Our results generalize some known ones.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219498816501899

Reference16 articles.

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2. Class-Preserving Automorphisms of Finite Groups

3. Local analysis of the normalizer problem

4. Class-Preserving Coleman Automorphisms of Finite Groups

5. Coleman automorphisms of finite groups