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 problems in class number two
Factorization results with combinatorial proofs.
Factorizations and Paige's theorem on complete maps.
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 of bounded rank with an almost regular automorphism of prime order.
Finite groups whose set of numbers of subgroups of possible order has exactly 2 elements
Counting subgroups of finite groups is one of the most important topics in finite group theory. We classify the finite non-nilpotent groups whose set of numbers of subgroups of possible orders has exactly two elements. We show that if is a non-nilpotent group whose set of numbers of subgroups of possible orders has exactly 2 elements, then has a normal Sylow subgroup of prime order and is solvable. Moreover, as an application we give a detailed description of non-nilpotent groups with...
Finite groups with eight non-linear irreducible characters
This Note contains the complete list of finite groups, having exactly eight non-linear irreducible characters. In section 4 we consider in full details some typical cases.
Finite groups with exactly thirteen conjugacy classes
Finite groups with few conjugacy classes of subgroups
Finite groups with few self-normalizing subgroups
We describe finite groups which contain just one conjugate class of self-normalizing subgroups.
Finite groups with prime graphs of diameter
In this paper we consider a prime graph of finite groups. In particular, we expect finite groups with prime graphs of maximal diameter.
Finite Groups with Small Conjugacy Classes.
Finite soluble and nilpotent groups with a restriction on the rank of the centralizer of an automorphism of prime order.
Fitting height of -nilpotent groups