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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
In this paper, we find a condition under which every chief factor of G below a normal subgroup E of G is cyclic by using the partial τ -quasinormality of some subgroups.
📌 3 Key Takeaways
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Objective & Hypothesis:Let H be a subgroup of a group G.
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Key Findings & Data:We say that: (1) H is τ -quasinormal in G if H permutes with every Sylow subgroup Q of G such that (|H|, |Q|) = 1 and (|H|, |Q G|) 6= 1; (2) H is partially τ -quasinormal in G if G has a normal subgroup T such that HT is S-quasinormal in G and H ∩ T ≤ HτG, where HτG is the subgroup generated by all those subgroups of H which are τ -quasinormal in G.
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Conclusion & Impact:In this paper, we find a condition under which every chief factor of G below a normal subgroup E of G is cyclic by using the partial τ -quasinormality of some subgroups.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:S-quasinormal · partially τ -quasinormal · cyclic
Abstract
Let H be a subgroup of a group G. We say that: (1) H is τ -quasinormal in G if H permutes with every Sylow subgroup Q of G such that (|H|, |Q|) = 1 and (|H|, |Q G|) 6= 1; (2) H is partially τ -quasinormal in G if G has a normal subgroup T such that HT is S-quasinormal in G and H ∩ T ≤ HτG, where HτG is the subgroup generated by all those subgroups of H which are τ -quasinormal in G. In this paper, we find a condition under which every chief factor of G below a normal subgroup E of G is cyclic by using the partial τ -quasinormality of some subgroups.
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Cite This Article
Li, C., Zhang, X., Yi, X. (2014). On partially τ-quasinormal subgroups of finite groups. Hacettepe Journal of Mathematics and Statistics, Volume: 43 Issue: 6. https://ajindex.com/articles/1403347