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Abnormal subgroups and Carter subgroups in some infinite groups
t. Some properties of abnormal subgroups in generalized soluble groups are considered. In particular, the transitivity of abnormality in metahypercentral groups is proven. Also it is proven that a subgroup H of a radical group G is abnormal in G if and only if every intermediate subgroup for H co...
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Інститут прикладної математики і механіки НАН України
2005
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| Series: | Algebra and Discrete Mathematics |
| Online Access: | http://dspace.nbuv.gov.ua/handle/123456789/156610 |
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irk-123456789-1566102019-06-19T01:29:31Z Abnormal subgroups and Carter subgroups in some infinite groups Kurdachenko, L.A. Subbotin, I.Ya. t. Some properties of abnormal subgroups in generalized soluble groups are considered. In particular, the transitivity of abnormality in metahypercentral groups is proven. Also it is proven that a subgroup H of a radical group G is abnormal in G if and only if every intermediate subgroup for H coincides with its normalizer in G. This result extends on radical groups the wellknown criterion of abnormality for finite soluble groups due to D. Taunt. For some infinite groups (not only periodic) the existence of Carter subgroups and their conjugation have been also obtained. 2005 Article Abnormal subgroups and Carter subgroups in some infinite groups / L.A. Kurdachenko, I.Ya. Subbotin // Algebra and Discrete Mathematics. — 2005. — Vol. 4, № 1. — С. 69–83. — Бібліогр.: 25 назв. — англ. 1726-3255 2000 Mathematics Subject Classification: 20E34, 20F19, 20F22. http://dspace.nbuv.gov.ua/handle/123456789/156610 en Algebra and Discrete Mathematics Інститут прикладної математики і механіки НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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DSpace DC |
| language |
English |
| description |
t. Some properties of abnormal subgroups in generalized soluble groups are considered. In particular, the transitivity
of abnormality in metahypercentral groups is proven. Also it is
proven that a subgroup H of a radical group G is abnormal in G
if and only if every intermediate subgroup for H coincides with its
normalizer in G. This result extends on radical groups the wellknown criterion of abnormality for finite soluble groups due to D.
Taunt. For some infinite groups (not only periodic) the existence
of Carter subgroups and their conjugation have been also obtained. |
| format |
Article |
| author |
Kurdachenko, L.A. Subbotin, I.Ya. |
| spellingShingle |
Kurdachenko, L.A. Subbotin, I.Ya. Abnormal subgroups and Carter subgroups in some infinite groups Algebra and Discrete Mathematics |
| author_facet |
Kurdachenko, L.A. Subbotin, I.Ya. |
| author_sort |
Kurdachenko, L.A. |
| title |
Abnormal subgroups and Carter subgroups in some infinite groups |
| title_short |
Abnormal subgroups and Carter subgroups in some infinite groups |
| title_full |
Abnormal subgroups and Carter subgroups in some infinite groups |
| title_fullStr |
Abnormal subgroups and Carter subgroups in some infinite groups |
| title_full_unstemmed |
Abnormal subgroups and Carter subgroups in some infinite groups |
| title_sort |
abnormal subgroups and carter subgroups in some infinite groups |
| publisher |
Інститут прикладної математики і механіки НАН України |
| publishDate |
2005 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/156610 |
| citation_txt |
Abnormal subgroups and Carter subgroups in some infinite groups / L.A. Kurdachenko, I.Ya. Subbotin // Algebra and Discrete Mathematics. — 2005. — Vol. 4, № 1. — С. 69–83. — Бібліогр.: 25 назв. — англ. |
| series |
Algebra and Discrete Mathematics |
| work_keys_str_mv |
AT kurdachenkola abnormalsubgroupsandcartersubgroupsinsomeinfinitegroups AT subbotiniya abnormalsubgroupsandcartersubgroupsinsomeinfinitegroups |
| first_indexed |
2023-05-20T17:50:07Z |
| last_indexed |
2023-05-20T17:50:07Z |
| _version_ |
1796154195053641728 |