Add to ORKGAbstract. Let G be a finite group of even order. We give some bounds for the probability p(G) that a randomly chosen element in G has a square root. In partic-ular, we prove that p(G) ≤ 1 − b√|G|c/|G|. Moreover, we show that if the Sylow 2-subgroup of G is not a proper normal elementary abelian subgroup of G, then p(G) ≤ 1 − 1/√|G|. Both of these bounds are best possible upper bounds for p(G), depending only on the order of G. 1
Abstract. In this paper we study the probability that the commutator of two randomly chosen elements...
This paper applies the theory of probability to finite groups. Three problems are addressed: the pro...
For a finite group $G$, let $d(G)$ denote the probability that a randomly chosen pair of elements of...
Abstract. Let G be a finite group of even order. We give some bounds for the probability p(G) that a...
In this paper, we study the probability that a randomly chosen element in a finite group has a squar...
The probability that a randomly chosen element has a square root is studied in [1, 2, 8] in the fini...
AbstractWe prove that a randomly chosen involution and a randomly chosen additional element of a fin...
Given a finite group G; let e(G) be the expected number of elements of G which have to be drawn at r...
The determination of the abelianness of a nonabelian group has been introduced for symmetric groups ...
For a finite group group, denote by V(G) the smallest positive integer k with the property that the ...
Let G be a finite group and let A be its automorphism group. We obtain various results on the probab...
Let G be a prosolvable group with all the Sylow subgroups d-generated. We give the best upper bound...
Let G be a finite soluble group of order m and let ω(xi, ⋯, xn) be a group word. Then the probabilit...
In this paper , we consider the probability that two elements chosen at random from a finite group G...
AbstractIn this paper we study the probability that the commutator of two randomly chosen elements i...
Abstract. In this paper we study the probability that the commutator of two randomly chosen elements...
This paper applies the theory of probability to finite groups. Three problems are addressed: the pro...
For a finite group $G$, let $d(G)$ denote the probability that a randomly chosen pair of elements of...
Abstract. Let G be a finite group of even order. We give some bounds for the probability p(G) that a...
In this paper, we study the probability that a randomly chosen element in a finite group has a squar...
The probability that a randomly chosen element has a square root is studied in [1, 2, 8] in the fini...
AbstractWe prove that a randomly chosen involution and a randomly chosen additional element of a fin...
Given a finite group G; let e(G) be the expected number of elements of G which have to be drawn at r...
The determination of the abelianness of a nonabelian group has been introduced for symmetric groups ...
For a finite group group, denote by V(G) the smallest positive integer k with the property that the ...
Let G be a finite group and let A be its automorphism group. We obtain various results on the probab...
Let G be a prosolvable group with all the Sylow subgroups d-generated. We give the best upper bound...
Let G be a finite soluble group of order m and let ω(xi, ⋯, xn) be a group word. Then the probabilit...
In this paper , we consider the probability that two elements chosen at random from a finite group G...
AbstractIn this paper we study the probability that the commutator of two randomly chosen elements i...
Abstract. In this paper we study the probability that the commutator of two randomly chosen elements...
This paper applies the theory of probability to finite groups. Three problems are addressed: the pro...
For a finite group $G$, let $d(G)$ denote the probability that a randomly chosen pair of elements of...