Influence of partially τ-embedded subgroups of prime power order in supersolubility and p-nilpotency of finite groups
In this paper, we introduced a new concept of $p\tau $ embedded subgroups which belongs to an embedded class of subgroups of finite groups. A subgroup H of a group G is said to be a partially τ-embedded subgroup in G if there exists a normal subgroup K of G such that HK is normal in G and $H \cap K...
| Published in: | Journal of Taibah University for Science |
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| Main Authors: | , , , |
| Format: | Article |
| Language: | English |
| Published: |
Taylor & Francis Group
2019-12-01
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| Subjects: | |
| Online Access: | http://dx.doi.org/10.1080/16583655.2019.1676940 |
| Summary: | In this paper, we introduced a new concept of $p\tau $ embedded subgroups which belongs to an embedded class of subgroups of finite groups. A subgroup H of a group G is said to be a partially τ-embedded subgroup in G if there exists a normal subgroup K of G such that HK is normal in G and $H \cap K \leq H_{p\tau G} $ where $H_{p\tau G} $ generated by all those subgroups of H which are partially τ-quasinormal in G. We investigate the influence of some $p\tau $-embedded subgroups with prime power order on the structure of a finite group G. Some new criteria about the p-nilpotency and supersolubility of a finite group were obtained. Our results also generalized some earlier ones about formations. |
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| ISSN: | 1658-3655 |