Add to ORKGThe determination of the abelianness of a nonabelian group has been introduced for symmetric groups by Erdos and Turan in 1968. In 1973, Gustafson did the same for finite groups while MacHale determined the abelianness for finite rings in 1974. Basic probability theory will be used in connection with group theory. This paper will focus on the 2-generator 2-groups of nilpotency class 2 based on the classification that has been done by Kappe et.al in 1999. In this paper some results on Pn(G), the probability that the nth power of a random element in a group G commutes with another random element from the same group, will be presented
In a profinite group G, we study the set of elements x with the following property: the probability ...
AbstractWe prove that a randomly chosen involution and a randomly chosen additional element of a fin...
Introduction. Let (G,+) be a finite Abelian group of order n. Let us choose k arbitrary elements gl,...
This paper applies the theory of probability to finite groups. Three problems are addressed: the pro...
In this paper we survey, also in historical perspective, the results connected with the notion of th...
A group G is metabelian if and only if there exists an abelian normal subgroup, A such that the fact...
This survey discusses three aspects of the ways in which probability has been applied to the theory ...
In this paper , we consider the probability that two elements chosen at random from a finite group G...
Let G be a finite group and let A be its automorphism group. We obtain various results on the probab...
Abstract. We give explicit, asymptotically sharp bounds for the probability that a pair of random pe...
AbstractWe prove the following conjecture of J. D. Dixon: The probability that a pair of random perm...
In several papers the probability that t randomly chosen elements of a group G generate G itself has...
Let L be a finite group with a unique minimal normal subgroup, say N. We study the conditional proba...
Dedicated to the memory of A. Rcenyi. Introduction. Let (G,+) be a finite Abelian group of order n, ...
In finite groups the probability that two randomly chosen elements commute or randomly ordered n−tup...
In a profinite group G, we study the set of elements x with the following property: the probability ...
AbstractWe prove that a randomly chosen involution and a randomly chosen additional element of a fin...
Introduction. Let (G,+) be a finite Abelian group of order n. Let us choose k arbitrary elements gl,...
This paper applies the theory of probability to finite groups. Three problems are addressed: the pro...
In this paper we survey, also in historical perspective, the results connected with the notion of th...
A group G is metabelian if and only if there exists an abelian normal subgroup, A such that the fact...
This survey discusses three aspects of the ways in which probability has been applied to the theory ...
In this paper , we consider the probability that two elements chosen at random from a finite group G...
Let G be a finite group and let A be its automorphism group. We obtain various results on the probab...
Abstract. We give explicit, asymptotically sharp bounds for the probability that a pair of random pe...
AbstractWe prove the following conjecture of J. D. Dixon: The probability that a pair of random perm...
In several papers the probability that t randomly chosen elements of a group G generate G itself has...
Let L be a finite group with a unique minimal normal subgroup, say N. We study the conditional proba...
Dedicated to the memory of A. Rcenyi. Introduction. Let (G,+) be a finite Abelian group of order n, ...
In finite groups the probability that two randomly chosen elements commute or randomly ordered n−tup...
In a profinite group G, we study the set of elements x with the following property: the probability ...
AbstractWe prove that a randomly chosen involution and a randomly chosen additional element of a fin...
Introduction. Let (G,+) be a finite Abelian group of order n. Let us choose k arbitrary elements gl,...
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