On connected transversals to Abelian subgroups

Connected transversals to subnormal subgroups

Subnormal subgroups possessing connected transversals are briefly discussed.

On Connected Transversals to Subgroups Whose Order is a Product of Two Primes

We consider finite groups which have connected transversals to subgroups whose order is a product of two primes p and q. We investigate those values of p and q for which the group is soluble. We can show that the solubility of the group follows if q = 2 and p ≤ 61, q = 3 and p ≤ 31, q = 5 and p ≤ 11. We then apply our results on loop theory and we show that if the inner mapping group of a finit...

Connected transversals to nilpotent groups

We prove that a finite group with nilpotent subgroup H and H-connected transversals is solvable. The proof depends on the classification of finite simple groups.

On non-normal non-abelian subgroups of finite groups

‎In this paper we prove that a finite group $G$ having at most three‎ ‎conjugacy classes of non-normal non-abelian proper subgroups is‎ ‎always solvable except for $Gcong{rm{A_5}}$‎, ‎which extends Theorem 3.3‎ ‎in [Some sufficient conditions on the number of‎ ‎non-abelian subgroups of a finite group to be solvable‎, ‎Acta Math‎. ‎Sinica (English Series) 27 (2011) 891--896.]‎. ‎Moreover‎, ‎we s...

On N-high Subgroups of Abelian Groups