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2013•Journal of Algebra and Its ApplicationsRequires access

COLEMAN AUTOMORPHISMS OF STANDARD WREATH PRODUCTS OF NILPOTENT GROUPS BY GROUPS WITH PRESCRIBED SYLOW 2-SUBGROUPS

Zhengxing Li, Jinke Hai

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Abstract

Let G = N wr H be the standard wreath product of N by H, where N is a finite nilpotent group and H is a finite group whose Sylow 2-subgroups are either cyclic, dihedral or generalized quaternion. It is shown that every Coleman automorphism of G is inner. As a direct consequence of this result, it is obtained that the normalizer property holds for G.

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What this paper is about

Let G = N wr H be the standard wreath product of N by H, where N is a finite nilpotent group and H is a finite group whose Sylow 2-subgroups are either cyclic, dihedral or generalized quaternion. It is shown that every Coleman automorphism of G is inner. As a direct consequence of this result, it is obtained that the normalizer property holds for G.

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OpenAlex reports 4 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

Let G = N wr H be the standard wreath product of N by H, where N is a finite nilpotent group and H is a finite group whose Sylow 2-subgroups are either cyclic, dihedral or generalized quaternion. It is shown that every Coleman automorphism of G is inner. As a direct consequence of this result, it is obtained that the normalizer property holds for G.

Key concepts: Mathematics, Wreath product, Sylow theorems, Automorphism, p-group, Centralizer and normalizer, Finite group, Nilpotent

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