Coleman automorphisms of holomorphs of completely reducible and almost simple groups

被引：0

作者：

Li, Zhengxing ^{[1
]}

机构：

[1] Qingdao Univ, Sch Math & Stat, Qingdao 266071, Peoples R China

来源：

PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES | 2018年 / 128卷 / 05期

基金：

中国国家自然科学基金; 高等学校博士学科点专项科研基金;

关键词：

Coleman automorphism; completely reducible group; almost simple group; the normalizer conjecture;

D O I：

10.1007/s12044-018-0432-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let H be the holomorph of a finite group G. It is proved that every Coleman automorphism of H is inner whenever G is either completely reducible or almost simple; in particular, this is the case when G is either characteristically simple or simple. As an application, we obtain the normalizer the conjecture holds for integral group rings of holomorphs of such groups in question.

引用

页数：9

共 50 条

[21] On Coleman Automorphisms of Extensions of Finite Quasinilpotent Groups by Some Groups
Hai, Jinke
Zhu, Yixin
[J]. ALGEBRA COLLOQUIUM, 2018, 25 (02) : 181 - 188
[22] ARTINIAN, ALMOST ABELIAN GROUPS AND THEIR GROUPS OF AUTOMORPHISMS
SCHLETTE, A
[J]. PACIFIC JOURNAL OF MATHEMATICS, 1969, 29 (02) : 403 - &
[23] Braiding groups of automorphisms and almost-automorphisms of trees
Skipper, Rachel
Zaremsky, Matthew C. B.
[J]. CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 2024, 76 (02): : 555 - 593
[24] On the orders of composition factors in completely reducible groups
Maroti, Attila
V. Skresanov, Saveliy
[J]. JOURNAL OF ALGEBRA, 2024, 645 : 183 - 196
[25] Class-preserving Coleman automorphisms of Frobenius groups
Li, Zhengxing
Li, Yuanlin
[J]. PUBLICATIONES MATHEMATICAE DEBRECEN, 2024, 105 (1-2): : 59 - 66
[26] Class-Preserving Coleman Automorphisms of Finite Groups
Martin Hertweck
[J]. Monatshefte für Mathematik, 2002, 136 : 1 - 7
[27] Determinateness of torsion-free abelian groups by their holomorphs and almost holomorphic isomorphism
Grinshpon S.Y.
Grinshpon I.E.
[J]. Journal of Mathematical Sciences, 2014, 197 (5) : 605 - 613
[28] Class-preserving coleman automorphisms of finite groups
Hertweck, M
[J]. MONATSHEFTE FUR MATHEMATIK, 2002, 136 (01): : 1 - 7
[29] Coleman automorphisms of finite groups and their minimal normal subgroups
Van Antwerpen, Arne
[J]. JOURNAL OF PURE AND APPLIED ALGEBRA, 2018, 222 (11) : 3379 - 3394
[30] On Coleman automorphisms of wreath products of finite nilpotent groups by abelian groups
Hai JinKe
Li ZhengXing
[J]. SCIENCE CHINA-MATHEMATICS, 2011, 54 (10) : 2253 - 2257

← 1 2 3 4 5 →