Soluble groups with few orbits under automorphisms

被引：1

作者：

Bastos, Raimundo ^{[1
]}

Dantas, Alex C. ^{[1
]}

de Melo, Emerson ^{[1
]}

机构：

[1] Univ Brasilia, Dept Matemat, BR-70910900 Brasilia, DF, Brazil

来源：

GEOMETRIAE DEDICATA | 2020年 / 209卷 / 01期

关键词：

Extensions; Automorphisms; Soluble groups;

D O I：

10.1007/s10711-020-00525-7

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let G be a group. The orbits of the natural action of Aut(G) on G are called "automorphism orbits" of G, and the number of automorphism orbits of G is denoted by.(G). We prove that if G is a soluble group of finite rank such that (G) < 8, then G contains a torsionfree radicable nilpotent characteristic subgroup K such that G = K H, where H is a finite group. Moreover, we classify the mixed order soluble groups of finite rank such that.(G) = 3.

引用

页码：119 / 123

页数：5

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