Let G be a finite group and let H be a subgroup of G. H is said to be an NR^*-subgroup of G if there exists a normal subgroup T of G such that G = HT and if whenever K \lhd H and g \in G, then K^g \cap H \cap T\leq K. A number of new characterizations of a group G are given, under the assumption that all Sylow subgroups of certain subgroups of G are NR^*-subgroups.
Finite group, NR^*-subgroup, the generalized Fitting subgroup, saturated formation
"On NR^*-subgroups of finite groups,"
Turkish Journal of Mathematics: Vol. 38:
2, Article 6.
Available at: https://journals.tubitak.gov.tr/math/vol38/iss2/6