A Rédei type factorization result for a special 2-group.
The size of an annihilator in a factorization.
A Hajós-type result on factoring finite Abelian groups by subsets.
An axiomatic approach for the Hajós theorem.
Factorization results with combinatorial proofs.
Factoring a finite Abelian group by prime complexes.
Factoring by nonsubgroup factors.
A Hajós type result on factoring finite abelian groups by subsets. II
It is proved that if a finite abelian group is factored into a direct product of lacunary cyclic subsets, then at least one of the factors must be periodic. This result generalizes Hajós's factorization theorem.
Equivalent conditions for p-nilpotence
In the first part of this paper we prove without using the transfer or characters the equivalence of some conditions, each of which would imply p-nilpotence of a finite group G. The implication of p-nilpotence also can be deduced without the transfer or characters if the group is p-constrained. For p-constrained groups we also prove an equivalent condition so that should be p-nilpotent. We show an example that this result is not true for some non-p-constrained groups. In the second part of the...
Page 1