A characterization of alternating groups by the set of orders of maximal Abelian subgroups.
Let G be a finite group, and (p ≥ 3). It is proved that G ≅ M if G and M have the same order components.
For a finite group and a fixed Sylow -subgroup of , Ballester-Bolinches and Guo proved in 2000 that is -nilpotent if every element of with order lies in the center of and when , either every element of with order lies in the center of or is quaternion-free and is -nilpotent. Asaad introduced weakly pronormal subgroup of in 2014 and proved that is -nilpotent if every element of with order is weakly pronormal in and when , every element of with order is also...
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