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Finite groups with semi-subnormal Schmidt subgroups

2020
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Algebra and discrete mathematics
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A b s t r ac t . A Schmidt group is a non-nilpotent group in which every proper subgroup is nilpotent. A subgroup A of a group G is semi-normal in G if there exists a subgroup B of G such that G = AB and AB 1 is a proper subgroup of G for every proper subgroup B 1 of B. If A is either subnormal in G or is semi-normal in G, then A is called a semi-subnormal subgroup of G. In this paper, we establish that a group G with semi-subnormal Schmidt {2, 3}-subgroups is 3-soluble. Moreover, if all

doi:10.12958/adm1376
fatcat:ifv4w6ldyreyhkws2gkc4cqnja