A note on the supersolubility of a group with ms-supersoluble factors
Tóm tắt
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. Let G be a supersoluble group. Then it has an ordered Sylow tower of supersoluble type
$$1=G_0< G_1< \cdots < G_m=G$$
. If for every i all maximal subgroups of
$$G_{i}/G_{i-1}$$
are seminormal in
$$G/G_{i-1}$$
, then G is said to be ms-supersoluble. In this paper, we proved the supersolubility of a group
$$G=AB$$
under condition that A and B are normal in G and ms-supersoluble.
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