TY - JOUR
AU - Yi Xiaolan
AU - Yang Xue
PY - 2015/12/25
Y2 - 2024/06/23
TI - Finite groups with X-quasipermutable Sylow subgroups
JF - Ukrains’kyi Matematychnyi Zhurnal
JA - Ukr. Mat. Zhurn.
VL - 67
IS - 12
SE - Research articles
DO -
UR - https://umj.imath.kiev.ua/index.php/umj/article/view/2104
AB - Let H ≤ E and X be subgroups of a finite group G. Then we say that H is X-quasipermutable (XS-quasipermutable,respectively) in E provided that G has a subgroup B such that E = NE(H)B and H X-permutes with B and with all subgroups (with all Sylow subgroups, respectively) V of B such that (|H|, |V |) = 1. We analyze the influence of X-quasipermutable and XS-quasipermutable subgroups on the structure of G. In particular, it is proved that if every Sylow subgroup P of G is F(G)-quasipermutable in its normal closure PG in G, then G is supersoluble.
ER -