Groups with many generalized FC-subgroup
Let FC⁰ be the class of all finite groups, and for each non-negative integer n define by induction the group class FCⁿ⁺¹ consisting of all groups G such that the factor group G/CG(xG) has the property FCⁿ for all elements x of G. Clearly, FC¹ is the class of FC-groups and every nilpotent group with...
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| Veröffentlicht in: | Algebra and Discrete Mathematics |
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| Datum: | 2009 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
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Інститут прикладної математики і механіки НАН України
2009
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/154643 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Groups with many generalized FC-subgroup / A. Russo, G. Vincenzi // Algebra and Discrete Mathematics. — 2009. — Vol. 8, № 4. — С. 158–166. — Бібліогр.: 17 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862661591040786432 |
|---|---|
| author | Russo, A. Vincenzi, G. |
| author_facet | Russo, A. Vincenzi, G. |
| citation_txt | Groups with many generalized FC-subgroup / A. Russo, G. Vincenzi // Algebra and Discrete Mathematics. — 2009. — Vol. 8, № 4. — С. 158–166. — Бібліогр.: 17 назв. — англ. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| description | Let FC⁰ be the class of all finite groups, and for each non-negative integer n define by induction the group class FCⁿ⁺¹ consisting of all groups G such that the factor group G/CG(xG) has the property FCⁿ for all elements x of G. Clearly, FC¹ is the class of FC-groups and every nilpotent group with class at most m belongs to FCm. The class of FCⁿ-groups was introduced in [6]. In this article the structure of groups with finitely many normalizers of non-FCⁿ-subgroups (respectively, the structure of groups whose subgroups either are subnormal with bounded defect or have the property FCⁿ) is investigated.
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| first_indexed | 2025-12-02T12:22:37Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-154643 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-12-02T12:22:37Z |
| publishDate | 2009 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Russo, A. Vincenzi, G. 2019-06-15T17:11:33Z 2019-06-15T17:11:33Z 2009 Groups with many generalized FC-subgroup / A. Russo, G. Vincenzi // Algebra and Discrete Mathematics. — 2009. — Vol. 8, № 4. — С. 158–166. — Бібліогр.: 17 назв. — англ. 1726-3255 2000 Mathematics Subject Classification:20F24. https://nasplib.isofts.kiev.ua/handle/123456789/154643 Let FC⁰ be the class of all finite groups, and for each non-negative integer n define by induction the group class FCⁿ⁺¹ consisting of all groups G such that the factor group G/CG(xG) has the property FCⁿ for all elements x of G. Clearly, FC¹ is the class of FC-groups and every nilpotent group with class at most m belongs to FCm. The class of FCⁿ-groups was introduced in [6]. In this article the structure of groups with finitely many normalizers of non-FCⁿ-subgroups (respectively, the structure of groups whose subgroups either are subnormal with bounded defect or have the property FCⁿ) is investigated. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics Groups with many generalized FC-subgroup Article published earlier |
| spellingShingle | Groups with many generalized FC-subgroup Russo, A. Vincenzi, G. |
| title | Groups with many generalized FC-subgroup |
| title_full | Groups with many generalized FC-subgroup |
| title_fullStr | Groups with many generalized FC-subgroup |
| title_full_unstemmed | Groups with many generalized FC-subgroup |
| title_short | Groups with many generalized FC-subgroup |
| title_sort | groups with many generalized fc-subgroup |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/154643 |
| work_keys_str_mv | AT russoa groupswithmanygeneralizedfcsubgroup AT vincenzig groupswithmanygeneralizedfcsubgroup |