EULER CHARACTERISTICS ON A CLASS OF FINITELY GENERATED NILPOTENT GROUPS

Hamrouni, Hatem

doi:info:doi/10.18910/25090

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タイトル	EULER CHARACTERISTICS ON A CLASS OF FINITELY GENERATED NILPOTENT GROUPS
著者	Hamrouni, Hatem Hamrouni, Hatem
抄録	A finitely generated torsion free nilpotent group is called an F-group. To each F-group Γ there is associated a connected, simply connected nilpotent Lie group G_Γ. Let TUF be the class of all F-group Γ such that G_Γ is totally unimodular. A group in TUF is called TUF-group. In this paper, we are interested in finding non-zero Euler characteristic on the class TUF and therefore, on TUFF, the class of groups K having a subgroup Γ of finite index in TUF. An immediate consequence we obtain that any two isomorphic finite index subgroups of a TUFF-group have the same index. As applications, we give two results, the first is a generalization of Belegradek's result, in which we prove that every TUFF-group is co-hopfian. The second is a known result due to G.C. Smith, asserting that every TUFF-group is not compressible.
公開者	Osaka University and Osaka City University, Departments of Mathematics
掲載誌名	Osaka Journal of Mathematics
巻	50
号	2
開始ページ	339
終了ページ	346
刊行年月	2013-06
ISSN	00306126
NCID	AA00765910
URL	http://hdl.handle.net/11094/25090
言語	英語
DOI	info:doi/10.18910/25090
カテゴリ	紀要論文 Departmental Bulletin Paper
カテゴリ	Osaka Journal of Mathematics / Volume 50, Number 2　(2013-6）

著者版フラグ	publisher
NII資源タイプ	紀要論文
ローカル資源タイプ	紀要論文
dcmi資源タイプ	text
DCTERMS.bibliographicCitation	Osaka Journal of Mathematics.50(2) P.339-P.346
DC.title	EULER CHARACTERISTICS ON A CLASS OF FINITELY GENERATED NILPOTENT GROUPS
DC.creator	Hamrouni, Hatem
DC.publisher	Osaka University and Osaka City University, Departments of Mathematics
DC.language" scheme="DCTERMS.RFC1766	英語
DCTERMS.issued" scheme="DCTERMS.W3CDTF	2013-06
DC.identifier" scheme="DCTERMS.URI	http://hdl.handle.net/11094/25090
DCTERMS.abstract	A finitely generated torsion free nilpotent group is called an F-group. To each F-group Γ there is associated a connected, simply connected nilpotent Lie group G_Γ. Let TUF be the class of all F-group Γ such that G_Γ is totally unimodular. A group in TUF is called TUF-group. In this paper, we are interested in finding non-zero Euler characteristic on the class TUF and therefore, on TUFF, the class of groups K having a subgroup Γ of finite index in TUF. An immediate consequence we obtain that any two isomorphic finite index subgroups of a TUFF-group have the same index. As applications, we give two results, the first is a generalization of Belegradek's result, in which we prove that every TUFF-group is co-hopfian. The second is a known result due to G.C. Smith, asserting that every TUFF-group is not compressible.
DC.identifier	info:doi/10.18910/25090
citation_title	EULER CHARACTERISTICS ON A CLASS OF FINITELY GENERATED NILPOTENT GROUPS
citation_author	Hamrouni, Hatem
citation_publisher	Osaka University and Osaka City University, Departments of Mathematics
citation_language	英語
citation_date	2013-06
citation_journal_title	Osaka Journal of Mathematics
citation_volume	50
citation_issue	2
citation_firstpage	339
citation_lastpage	346
citation_issn	00306126
citation_public_url	http://hdl.handle.net/11094/25090
citation_doi	info:doi/10.18910/25090

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