On weakly Π-embedded subgroups of finite groups
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Abstract
Let G be a finite group and H a subgroup of G. H is called weakly Π-embedded in G if there exists a subgroup pair (T, S), where T is a quasinormal subgroup of G containing HG and S/HG≤H/HG satisfies Π-property in G/HG, such that |G:HT| is a power of a prime and (H∩T)/HG≤S/HG. Here weakly Π-embedded subgroups were used to explore the structure of finite groups. In particular, new criterions of hypercyclically embedded subgroups were obtained.
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