Characterizations of some wreath products of groups by their endomorphism semigroups

被引：1

作者：

Puusemp, Peeter ^{[1
]}

机构：

[1] Tallinn Univ Technol, Dept Math, EE-19086 Tallinn, Estonia

来源：

INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION | 2008年 / 18卷 / 02期

关键词：

group; semigroup; endomorphism; automorphism;

D O I：

10.1142/S0218196708004421

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let A be a cyclic group of order p(n), where p is a prime, and B be a finite abelian group or a finite p-group which is determined by its endomorphism semigroup in the class of all groups. It is proved that under these assumptions the wreath product A Wr B is determined by its endomorphism semigroup in the class of all groups. It is deduced from this result that if A, B, A(0),..., A(n) are finite abelian groups and A(0),..., An are p-groups, p prime, then the wreath products A Wr B and A(n) Wr (...( Wr ( A(1) Wr A(0)))...) are determined by their endomorphism semigroups in the class of all groups.

引用

页码：243 / 255

页数：13

共 11 条

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