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Cyclic subgroup separability of certain graph products of subgroup separable groups

Peng Choon Wong|Kok Bin Wong
대한수학회 (The Korean Mathematical Society)|2013.09|대한수학회보 (Bulletin of the KMS)|제50권 제5호|pp. 1753-1763

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참고문헌

키워드

subgroup separablecyclic subgroup separabilitygraph productspolycyclic-by-finite groups
주제분류수학

초록

In this paper, we show that tree products ofcertain subgroup separable groups amalgamating normal subgroups are cyclic subgroup separable. We then extend this result to certain graph product of certain subgroup separable groups amalgamating normal subgroups, that is we show that if the graph has exactly one cycle and the cycle is of length at least four, then the graph product is cyclic subgroup separable.

Abstract

In this paper, we show that tree products ofcertain subgroup separable groups amalgamating normal subgroups are cyclic subgroup separable. We then extend this result to certain graph product of certain subgroup separable groups amalgamating normal subgroups, that is we show that if the graph has exactly one cycle and the cycle is of length at least four, then the graph product is cyclic subgroup separable.

참고문헌 (32)

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관련 논문AI추천

WEAK POTENCY AND CYCLIC SUBGROUP SEPARABILITY OF CERTAIN FREE PRODUCTS AND TREE PRODUCTSKok Bin Wong, Muhammad Sufi Mohd Asri, Peng Choon Wong, Wan Ainun Mior Othman대한수학회 · 대한수학회보2023 · 제60권 제5호On the residual finiteness of fundamental groups of graphs of certain groups김관수대한수학회 · 대한수학회지2004 · 제41권 제5호Conjugacy separability of certain generalized free products of nilpotent groups김관수, C. Y. Tang대한수학회 · 대한수학회지2013 · 제50권 제4호Outer automorphism groups of polygonal products of certain conjugacy separable groups김관수, Chi Yu Tang대한수학회 · 대한수학회지2008 · 제45권 제6호CONJUGACY SEPARABILITY OF GENERALIZED FREE PRODUCTS OF FINITELY GENERATED NILPOTENT GROUPS김관수, C. Y. Tang, Wei Zhou, Wujie Shi대한수학회 · 대한수학회보2010 · 제47권 제6호On the residual finiteness of certain polygonal products of free groups김관수대한수학회 · 대한수학회논문집2016 · 제31권 제3호

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