Some Results on ICΦ-subgroups and p-supersolvable Hypercenter
A subgroup H of a group G is called an ICΦ-subgroup of G if H ∩[H,G]≤Φ(H),where Φ(H)is the Frattini subgroup of H.Based on this concept,firstly,for odd prime numbers,by the p-nilpotent result of Kaspczyk,we analyzed the influence of the ICΦ-properties of subgroups with a given order on the structure of p-supersolvable hypercenter.Secondly,we determined the types of all ICΦ-subgroups in the symmetric group S5.These results will provide specific examples for the study of ICΦ-properties of subgroups,and also make positive attempts to enrich the research of this topic.
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