Finite groups with X-quasipermutable Sylow subgroups
Let H ≤ E and X be subgroups of a finite group G. Then we say that H is X-quasipermutable (XS-quasipermutable, respectively) in E provided that G has a subgroup B such that E = NE(H)B and H X-permutes with B and with all subgroups (with all Sylow subgroups, respectively) V of B such that (|H|, |V |)...
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| Datum: | 2015 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Інститут математики НАН України
2015
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| Schriftenreihe: | Український математичний журнал |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Finite groups with X-quasipermutable Sylow subgroups / Xiaolan Yi, Xue Yang// Український математичний журнал. — 2015. — Т. 67, № 12. — С. 1715–1722. — Бібліогр.: 12 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | Let H ≤ E and X be subgroups of a finite group G. Then we say that H is X-quasipermutable (XS-quasipermutable, respectively) in E provided that G has a subgroup B such that E = NE(H)B and H X-permutes with B and with all subgroups (with all Sylow subgroups, respectively) V of B such that (|H|, |V |) = 1. We analyze the influence of X-quasipermutable and XS-quasipermutable subgroups on the structure of G. In particular, it is proved that if every Sylow subgroup P of G is F(G)-quasipermutable in its normal closure PG in G, then G is supersoluble. |
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