Factoring Abelian groups of order .
Factoring an odd abelian group by lacunary cyclic subsets
It is a known result that if a finite abelian group of odd order is a direct product of lacunary cyclic subsets, then at least one of the factors must be a subgroup. The paper gives an elementary proof that does not rely on characters.
Factoring by nonsubgroup factors.
Factorization of groups involving symmetric and alternating groups.
Factorization problems in class number two
Factorization results with combinatorial proofs.
Factorizations and Paige's theorem on complete maps.
Factorizations of Finite Groups.
Factorizations of one-generated -local formations.
Finite abelian groups and factorization problems. II
Finite coverings of groups
Finite groups admitting some coprime operator groups
Finite Groups as the Union of Proper Subgroups
2000 Mathematics Subject Classification: 20D60,20E15.As is known, if a finite solvable group G is an n-sum group then n − 1 is a prime power. It is an interesting problem in group theory to study for which numbers n with n-1 > 1 and not a prime power there exists a finite n-sum group. In this paper we mainly study finite nonsolvable n-sum groups and show that 15 is the first such number. More precisely, we prove that there exist no finite 11-sum or 13-sum groups and there is indeed a finite 15-sum...
Finite Groups Generated by 3-Transpositions. I.
Finite Groups have local Non-Schur Centralizers.
Finite groups in which every self-centralizing subgroup is nilpotent or subnormal or a TI-subgroup
Let be a finite group. We prove that if every self-centralizing subgroup of is nilpotent or subnormal or a TI-subgroup, then every subgroup of is nilpotent or subnormal. Moreover, has either a normal Sylow -subgroup or a normal -complement for each prime divisor of .
Finite groups in which every two elements generate a soluble subgroup.
Finite groups in which subnormalizers are subgroups
Finite groups in which Sylow normalizers have nilpotent Hall supplements.
Finite groups in which the normalizers of Sylow 3-subgroups are of odd or primary index.