LOCALIZED NEARLY m-EMBEDDED PROPERTY OF SOME SUBGROUPS OF FINITE GROUPS - Xu, Yong (Italian Journal of Pure and Applied Mathematics, 2013)
Let A be a subgroup of a finite group G and Σ : G0 ≤ G1 ≤ · · · ≤ Gn some subgroup series of G. Suppose that for each pair (K,H) such that K is a maximal subgroup of H and Gi−1 ≤ K < H ≤ Gi, for some i, either A ∩ H = A ∩ K or AH = AK. Then A is said to be Σ-embedded in G; A is said to be nearly m-embedded in G if G has a subgroup T and a 1 ≤ G-embedded subgroup C in G such that G = AT and T ∩ A ≤ C ≤ A. In this paper, we localize the above conditions in the G-normalizer of Sylow subgroups of the group G. Some new characterizations of some classes of finite groups are given.