JP Journal of Algebra, Number Theory and Applications
Volume 4, Issue 3, Pages 437 - 446
(December 2004)
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FINITE
GROUPS WITH SOME SUBGROUPS PERMUTABLE WITH ALL
SYLOW SUBGROUPS
M. Asaad (Egypt), A. A. Heliel (Egypt), M. Ezzat Mohamed (Egypt) and Piroska Csörgö (Hungary)
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Abstract: A subgroup of a group G
is said to be S-quasinormal in G if
it permutes with every Sylow subgroup of G.
A subgroup H of a group G is said
to be S-quasinormally embedded in G if
every Sylow subgroup of H is a Sylow
subgroup of some S-quasinormal subgroup
of G. In this paper we study the
structure of the finite group G under the
assumption that all maximal subgroups of the
Sylow subgroups of the generalized Fitting
subgroup of some normal subgroup of G are
S-quasinormally embedded in G. Our
results improve and extend the main results of
[Comm. Algebra 26 (1998), 3647-3652], [J. Pure
Appl. Algebra 165 (2001), 129-135], [Arch. Math.
56 (1991), 521-527], [J. Pure Appl. Algebra 127
(1998), 113-118], [Arch. Math. 81 (2003),
245-252], [Acta Math. Hungar. 59 (1992),
107-110] and [Israel J. Math. 35 (1980),
210-214]. |
Keywords and phrases: S-quasinormally
embedded subgroups, subnormally embedded, the
generalized Fitting subgroup, saturated formation. |
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