2020
DOI: 10.1515/jgth-2019-0177
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On the supersolubility of a group with semisubnormal factors

Abstract: A subgroup A of a group G is called seminormal in G if there exists a subgroup B such that {G=AB} and AX is a subgroup of G for every subgroup X of B. We introduce the new concept that unites subnormality and seminormality. A subgroup A of a group G is called semisubnormal in G if A is subnormal in G or seminormal in G. A group {G=AB} with semisubnormal supersoluble subgroups A and B is studied. The equality {G^{\mathfrak{U}}=(G^{\prime})^{\mathfrak{N}}} is established; moreover, if the indices of subgroups A … Show more

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