Groups with Bounded Chernikov Conjugate Classes of Elements
We consider BCC-groups, that is groups G with Chernikov conjugacy classes in which for every element x ∈ G the minimax rank of the divisible part of the Chernikov group G/C G(xᴳ) and the order of the corresponding factor-group are bounded in terms of G only. We prove that a BCC-group has a Chernikov...
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| Date: | 2002 |
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| Main Authors: | , , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2002
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| Series: | Український математичний журнал |
| Subjects: | |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Groups with Bounded Chernikov Conjugate Classes of Elements / L.A. Kurdachenko, J. Otal, I.Ya. Subbotin // Український математичний журнал. — 2002. — Т. 54, № 6. — С. 798–807. — Бібліогр.: 20 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | We consider BCC-groups, that is groups G with Chernikov conjugacy classes in which for every element x ∈ G the minimax rank of the divisible part of the Chernikov group G/C G(xᴳ) and the order of the corresponding factor-group are bounded in terms of G only. We prove that a BCC-group has a Chernikov derived subgroup. This fact extends the well-known result due to B. H. Neumann characterizing groups with bounded finite conjugacy classes (BFC-groups). |
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