On the finite groups of supersoluble type

On the finite groups of supersoluble type

We study the properties of finite groups in which every Sylow subgroup can be connected to the group by a chain of subgroups of prime indices. We establish the solubility of this type of groups. We prove that the class of all finite groups with this property of Sylow subgroups is a saturated heredit...

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Bibliographic Details
Published in:Siberian mathematical journal Vol. 51; no. 6; pp. 1004 - 1012
Main Authors: Vasil’ev, A.F., Vasil’eva, T.I., Tyutyanov, V.N.
Format: Journal Article
Language:English
Published: Dordrecht SP MAIK Nauka/Interperiodica 01-11-2010
Subjects:
Mathematics
Mathematics and Statistics
w-supersoluble group
finite group
saturated formation
P-subnormal subgroup
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Summary:We study the properties of finite groups in which every Sylow subgroup can be connected to the group by a chain of subgroups of prime indices. We establish the solubility of this type of groups. We prove that the class of all finite groups with this property of Sylow subgroups is a saturated hereditary formation. For these groups we find some analogs of the available theorems on the products of normal supersoluble subgroups.
ISSN:0037-4466
1573-9260
DOI:10.1007/s11202-010-0099-z