Normal subgroups of groups which split over the infinite cyclic group

被引：1

作者：

Moon, M ^{[1
]}

机构：

[1] Konkuk Univ, Dept Math Educ, Seoul 143701, South Korea

来源：

BULLETIN OF THE LONDON MATHEMATICAL SOCIETY | 2000年 / 32卷

关键词：

D O I：

10.1112/S0024609399006578

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let G be either a free product with amalgamation A *(C) B or an HNN group A*(C), where all normal subgroups of C are finitely generated. Suppose that both A and B have no non-trivial finitely generated normal subgroups of infinite indices. We show that if G contains a finitely generated normal subgroup N which intersects A or B non-trivially but is not contained in C, then the index of N in G is finite.

引用

页码：78 / 84

页数：7

共 7 条

[1]

[Anonymous], 1981, LECT NOTES MATH

[2] FINITELY GENERATED SUBGROUPS OF HNN GROUPS [J].

BURNS, RG .

CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 1973, 25 (05) :1103-1112

[3] FINITELY GENERATED SUBGROUPS OF AN AMALGAMATED PRODUCT OF 2 GROUPS [J].

BURNS, RG .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1972, 169 (NJUL) :293-&

[4]

Cohen D. E., 1976, Journal of the Australian Mathematical Society, Series A (Pure Mathematics), V22, P274

[5]

Cohen D.E., 1974, J AUSTRAL MATH SOC, V17, P394

[6]

Schreier O., 1927, ABH MATH SEM HAMBURG, V5, P161, DOI 10.1007/BF02952517

[7]

Scott P., 1979, London Math. Soc. Lecture Note Ser., V36, P137

← 1 →