Normal subgroups and p-regular G-class sizes

p-divisibility of conjugacy class sizes and normal p-complements

LetN be a normal subgroup of a groupG and let p be a prime. We prove that if the p-part of jx j is a constant for every prime-power order element x 2 N n Z.N /, then N is solvable and has normal p-complement.

Normal subgroups and class sizes of elements of prime power order∗

If G is a finite group and N is a normal subgroup of G with two Gconjugacy class sizes of elements of prime power order, then we show that N is nilpotent.

Normal Circulant Graphs with Noncyclic Regular Subgroups

ON p-NILPOTENCY OF FINITE GROUPS WITH SS-NORMAL SUBGROUPS

Abstract. A subgroup H of a group G is said to be SS-embedded in G if there exists a normal subgroup T of G such that HT is subnormal in G and H T H sG , where H sG is the maximal s- permutable subgroup of G contained in H. We say that a subgroup H is an SS-normal subgroup in G if there exists a normal subgroup T of G such that G = HT and H T H SS , where H SS is an SS-embedded subgroup of ...

Some results on g-regular and g-normal spaces

In this paper, map theorem and topological sum theorem on g-regular (resp. g-normal) spaces are given respectively, and their properties are discussed. In addition, Urysohn’s Lemma on g-normal spaces is proved.