Add to ORKGIt is well known that a ®nite group is soluble if each of its 2-generator subgroups is soluble (see Thompson [23] and Flavell [7]). Here we prove a probabilistic version of this result. Theorem A. Let G be a ®nite group
In [1] we obtained a short proof of the theorem of Thompson that a finite group is soluble if and on...
none3Let F be the free prosoluble group of rank d. We determine the minimum integer k such that the ...
none3Let F be the free prosoluble group of rank d. We determine the minimum integer k such that the ...
For a finite group group, denote by V(G) the smallest positive integer k with the property that the ...
We will prove the following result. Theorem Let G be a finite group in which every two elements gene...
This article is a survey of the author’s work on generation theorems for finite groups. The starting...
Let G be a finite soluble group of order m and let ω(xi, ⋯, xn) be a group word. Then the probabilit...
Let G be a finite soluble group of order m and let ω(xi, ⋯, xn) be a group word. Then the probabilit...
We prove that every finitely generated soluble group that is not virtuallyabelian has a subgroup of o...
We prove that every finitely generated soluble group that is not virtuallyabelian has a subgroup of o...
We prove that every finitely generated soluble group that is not virtually abelian has a subgroup of...
AbstractWe prove that if a finite soluble group G can be generated by s subgroups with pairwise copr...
We discuss some questions related to the generation of supersoluble groups. First we prove that the ...
We study the probability of generating a finite simple group, together with its generalisation PG,so...
We study the probability of generating a finite simple group, together with its generalisation PG,so...
In [1] we obtained a short proof of the theorem of Thompson that a finite group is soluble if and on...
none3Let F be the free prosoluble group of rank d. We determine the minimum integer k such that the ...
none3Let F be the free prosoluble group of rank d. We determine the minimum integer k such that the ...
For a finite group group, denote by V(G) the smallest positive integer k with the property that the ...
We will prove the following result. Theorem Let G be a finite group in which every two elements gene...
This article is a survey of the author’s work on generation theorems for finite groups. The starting...
Let G be a finite soluble group of order m and let ω(xi, ⋯, xn) be a group word. Then the probabilit...
Let G be a finite soluble group of order m and let ω(xi, ⋯, xn) be a group word. Then the probabilit...
We prove that every finitely generated soluble group that is not virtuallyabelian has a subgroup of o...
We prove that every finitely generated soluble group that is not virtuallyabelian has a subgroup of o...
We prove that every finitely generated soluble group that is not virtually abelian has a subgroup of...
AbstractWe prove that if a finite soluble group G can be generated by s subgroups with pairwise copr...
We discuss some questions related to the generation of supersoluble groups. First we prove that the ...
We study the probability of generating a finite simple group, together with its generalisation PG,so...
We study the probability of generating a finite simple group, together with its generalisation PG,so...
In [1] we obtained a short proof of the theorem of Thompson that a finite group is soluble if and on...
none3Let F be the free prosoluble group of rank d. We determine the minimum integer k such that the ...
none3Let F be the free prosoluble group of rank d. We determine the minimum integer k such that the ...