Strong convergence theorem of implicit iteration process for generalized asymptotically nonexpansive mappings in Hilbert space.
Convergence to common fixed point for generalized asymptotically nonexpansive semigroup in Banach spaces.
Strong convergence theorem for two commutative asymptotically nonexpansive mappings in Hilbert space.
Finite groups whose all proper subgroups are -groups
A group is said to be a -group if for every divisor of the order of , there exists a subgroup of of order such that is normal or abnormal in . We give a complete classification of those groups which are not -groups but all of whose proper subgroups are -groups.
Finite groups with some SS-supplemented subgroups
A subgroup of a finite group is said to be SS-supplemented in if there exists a subgroup of such that and is S-quasinormal in . We analyze how certain properties of SS-supplemented subgroups influence the structure of finite groups. Our results improve and generalize several recent results.
The -nilpotency of finite groups with some weakly pronormal subgroups
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...
A note on the -property of some subgroups of finite groups
Let be a subgroup of a finite group . We say that satisfies the -property in if for any chief factor of , is a -number. We obtain some criteria for the -supersolubility or -nilpotency of a finite group and extend some known results by concerning some subgroups that satisfy the -property.
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