2025-02-23T03:31:47-05:00 DEBUG: VuFindSearch\Backend\Solr\Connector: Query fl=%2A&wt=json&json.nl=arrarr&q=id%3A%22irk-123456789-165441%22&qt=morelikethis&rows=5
2025-02-23T03:31:47-05:00 DEBUG: VuFindSearch\Backend\Solr\Connector: => GET http://localhost:8983/solr/biblio/select?fl=%2A&wt=json&json.nl=arrarr&q=id%3A%22irk-123456789-165441%22&qt=morelikethis&rows=5
2025-02-23T03:31:47-05:00 DEBUG: VuFindSearch\Backend\Solr\Connector: <= 200 OK
2025-02-23T03:31:47-05:00 DEBUG: Deserialized SOLR response
Weakly SS-quasinormal minimal subgroups and the nilpotency of a finite group

Weakly SS-quasinormal minimal subgroups and the nilpotency of a finite group

A subgroup H is said to be an s-permutable subgroup of a finite group G provided that the equality HP =PH holds for every Sylow subgroup P of G. Moreover, H is called SS-quasinormal in G if there exists a supplement B of H to G such that H permutes with every Sylow subgroup of B. We show that H is w...

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Bibliographic Details
Main Authors: Zhao, T., Zhang, X.
Format: Article
Language:English
Published: Інститут математики НАН України 2014
Series:Український математичний журнал
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Online Access:http://dspace.nbuv.gov.ua/handle/123456789/165441
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Summary:A subgroup H is said to be an s-permutable subgroup of a finite group G provided that the equality HP =PH holds for every Sylow subgroup P of G. Moreover, H is called SS-quasinormal in G if there exists a supplement B of H to G such that H permutes with every Sylow subgroup of B. We show that H is weakly SS-quasinormal in G if there exists a normal subgroup T of G such that HT is s-permutable and H \ T is SS-quasinormal in G. We study the influence of some weakly SS-quasinormal minimal subgroups on the nilpotency of a finite group G. Numerous results known from the literature are unified and generalized.

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