In this note we present the following characterizations of finite abelian and minimal nonabelian groups: (i) A group G is abelian if and only if G\u27 = Φ(G)\u27. (ii) A group G is either abelian or minimal nonabelian if and only if Φ(G)\u27 = H\u27 for all maximal subgroups H of G. We also prove a number of related results
Let A be a finite group, and let p be a prime. Suppose that ps is the highest power of p dividing |A...
The p-groups all of whose nonabelian maximal subgroups are either absolutely regular or of maximal c...
Y. Berkovich has proposed to classify nonabelian finite p-groups G of exponent >p which have exactly...
In this note we present the following characterizations of finite abelian and minimal nonabelian gro...
We give here a complete classification (up to isomorphism) of the title groups (Theorems 1, 3 and 5)...
AbstractIn Theorem 2.1 we characterize finite p-groups G such that each nonabelian subgroup H of G w...
The number of prime factors of the order of a group G (multiplicities counted) is said to be the hei...
AbstractThis paper classifies the finite groups in which any nonmaximal abelian subgroups do not hav...
AbstractLet P be a Sylow p-subgroup and b(G) the largest irreducible character degree of a finite gr...
In this note alternate proofs of some basic results of finite group theory are presented
AbstractLet G be a group. We study the minimal sumset (or product set) size μG(r,s)=min{|A⋅B|}, wher...
We give here a complete classification (up to isomorphism) of the title groups (Theorem 1 and Theore...
We determine up to isomorphism finite non-Dedekindian p-groups G (i.e., p-groups which possess non-n...
AbstractIt is known that a (generalized) soluble group whose proper subgroups are abelian is either ...
Nonabelian nonmetacyclic finite 2-groups in which every proper subgroup is abelian or metacyclic and...
Let A be a finite group, and let p be a prime. Suppose that ps is the highest power of p dividing |A...
The p-groups all of whose nonabelian maximal subgroups are either absolutely regular or of maximal c...
Y. Berkovich has proposed to classify nonabelian finite p-groups G of exponent >p which have exactly...
In this note we present the following characterizations of finite abelian and minimal nonabelian gro...
We give here a complete classification (up to isomorphism) of the title groups (Theorems 1, 3 and 5)...
AbstractIn Theorem 2.1 we characterize finite p-groups G such that each nonabelian subgroup H of G w...
The number of prime factors of the order of a group G (multiplicities counted) is said to be the hei...
AbstractThis paper classifies the finite groups in which any nonmaximal abelian subgroups do not hav...
AbstractLet P be a Sylow p-subgroup and b(G) the largest irreducible character degree of a finite gr...
In this note alternate proofs of some basic results of finite group theory are presented
AbstractLet G be a group. We study the minimal sumset (or product set) size μG(r,s)=min{|A⋅B|}, wher...
We give here a complete classification (up to isomorphism) of the title groups (Theorem 1 and Theore...
We determine up to isomorphism finite non-Dedekindian p-groups G (i.e., p-groups which possess non-n...
AbstractIt is known that a (generalized) soluble group whose proper subgroups are abelian is either ...
Nonabelian nonmetacyclic finite 2-groups in which every proper subgroup is abelian or metacyclic and...
Let A be a finite group, and let p be a prime. Suppose that ps is the highest power of p dividing |A...
The p-groups all of whose nonabelian maximal subgroups are either absolutely regular or of maximal c...
Y. Berkovich has proposed to classify nonabelian finite p-groups G of exponent >p which have exactly...
DOI
Add to ORKG