AbstractLet G be a non-cyclic finite group that can be generated by two elements. A subset S of G is said to be a pairwise generating set for G if every distinct pair of elements in S generates G. The maximal size of a pairwise generating set for G is denoted by ω(G). The minimal number of proper subgroups of G whose union is G is denoted by σ(G). This is an upper bound for ω(G). In this paper we give lower bounds for ω(G) and upper bounds for σ(G) whenever G is a sporadic simple group
The spread of a group G is the greatest number r such that, for every set of non-trivial elements {x...
A group G is said to be 3/2-generated if every nontrivial element belongs to a generating pair. It i...
The spread of a group G is the greatest number r such that, for every set of non-trivial elements {x...
Abstract. Let G be a non-cyclic finite group that can be generated by two elements. A subset S of G ...
AbstractLet G be a non-cyclic finite group that can be generated by two elements. A subset S of G is...
It is well known that every finite simple group can be generated by two elements and this leads to a...
Let G be a finite group. It has recently been proved that every nontrivial element of G is contained...
Let G be a finite group. It has recently been proved that every nontrivial element of G is contained...
A generating set for a finite group G is minimal if no proper subset generates G, and m(G) denotes t...
AbstractA subset S of a finite group G invariably generates G if G=〈sg(s)|s∈S〉 for each choice of g(...
The generating graph Γ(G) of a finite group G is the graph defined on the elements of G with an edge...
Abstract. The generating graph Γ(G) of a finite group G is the graph defined on the elements of G wi...
In this thesis we consider two-element generation of certain permutation groups. Interest is focusse...
A group G is said to be 3/2-generated if every nontrivial element belongs to a generating pair. It i...
AbstractLet G be any of the groups (P)GL(n,q), (P)SL(n,q). Define a (simple) graph Γ=Γ(G) on the set...
The spread of a group G is the greatest number r such that, for every set of non-trivial elements {x...
A group G is said to be 3/2-generated if every nontrivial element belongs to a generating pair. It i...
The spread of a group G is the greatest number r such that, for every set of non-trivial elements {x...
Abstract. Let G be a non-cyclic finite group that can be generated by two elements. A subset S of G ...
AbstractLet G be a non-cyclic finite group that can be generated by two elements. A subset S of G is...
It is well known that every finite simple group can be generated by two elements and this leads to a...
Let G be a finite group. It has recently been proved that every nontrivial element of G is contained...
Let G be a finite group. It has recently been proved that every nontrivial element of G is contained...
A generating set for a finite group G is minimal if no proper subset generates G, and m(G) denotes t...
AbstractA subset S of a finite group G invariably generates G if G=〈sg(s)|s∈S〉 for each choice of g(...
The generating graph Γ(G) of a finite group G is the graph defined on the elements of G with an edge...
Abstract. The generating graph Γ(G) of a finite group G is the graph defined on the elements of G wi...
In this thesis we consider two-element generation of certain permutation groups. Interest is focusse...
A group G is said to be 3/2-generated if every nontrivial element belongs to a generating pair. It i...
AbstractLet G be any of the groups (P)GL(n,q), (P)SL(n,q). Define a (simple) graph Γ=Γ(G) on the set...
The spread of a group G is the greatest number r such that, for every set of non-trivial elements {x...
A group G is said to be 3/2-generated if every nontrivial element belongs to a generating pair. It i...
The spread of a group G is the greatest number r such that, for every set of non-trivial elements {x...
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