Add to ORKGA nite group G is said to be (l; m; n)-generated, if it is a quotient group of the triangle group T(l; m; n) = ⟨ x; y; zlxl = ym = zn = xyz = 1⟩ : In [28], Moori posed the question of nding all the (p; q; r) triples, where p; q and r are prime numbers, such that a non-abelian nite simple group G is (p; q; r)- generated. In this paper we will establish all the (p; q; r)-generations of the alternating group A10: GAP [24] and the Atlas of nite group representations [1] are used in our computations.Key words: Conjugacy classes, generation, structure constant, alternating groups
The nonabelian tensor square G⊗G of the group G is the group generated by the symbols g ⊗ h, where g...
AbstractLet G be any non-abelian group and Z(G) be its center. The non-commuting graph ΓG of G is th...
Suppose that G is a finite group and K is a non-trivial conjugacy class of G such that KK−1 = 1 ∪ D ...
AbstractAn (l,m,n)-generated groupGis a quotient group of the triangle groupT(l,m,n)=〈x,y,z∣xl=ym=zn...
summary:Let $G$ be a finite group, and let $N(G)$ be the set of conjugacy class sizes of $G$. By Tho...
AbstractAn (l,m,n)-generated groupGis a quotient group of the triangle groupT(l,m,n)=〈x,y,z|xl=ym=zn...
Given a finite group G, the invariably generating graph of G is defined as the undirected graph in w...
We classify the conjugacy classes of $p$-cycles of type D in alternating groups. This finishes the o...
AbstractA groupGis said to be 2-generated if it can be generated by two suitable elements. In this p...
In this thesis we consider two-element generation of certain permutation groups. Interest is focusse...
AbstractIt is shown that a collection of circular permutations of length three on an n-set generates...
In 1998, the second author raised the problem of classifying the irreducible characters of Sn of pri...
Abstract: A group G is said to be (2; 3; t)-generated if it can be generated by two elements x and y...
summary:For a finite group $G$ denote by $N(G)$ the set of conjugacy class sizes of $G$. In 1980s, J...
AbstractWe prove the Arad–Herzog conjecture for various families of finite simple groups — if A and ...
The nonabelian tensor square G⊗G of the group G is the group generated by the symbols g ⊗ h, where g...
AbstractLet G be any non-abelian group and Z(G) be its center. The non-commuting graph ΓG of G is th...
Suppose that G is a finite group and K is a non-trivial conjugacy class of G such that KK−1 = 1 ∪ D ...
AbstractAn (l,m,n)-generated groupGis a quotient group of the triangle groupT(l,m,n)=〈x,y,z∣xl=ym=zn...
summary:Let $G$ be a finite group, and let $N(G)$ be the set of conjugacy class sizes of $G$. By Tho...
AbstractAn (l,m,n)-generated groupGis a quotient group of the triangle groupT(l,m,n)=〈x,y,z|xl=ym=zn...
Given a finite group G, the invariably generating graph of G is defined as the undirected graph in w...
We classify the conjugacy classes of $p$-cycles of type D in alternating groups. This finishes the o...
AbstractA groupGis said to be 2-generated if it can be generated by two suitable elements. In this p...
In this thesis we consider two-element generation of certain permutation groups. Interest is focusse...
AbstractIt is shown that a collection of circular permutations of length three on an n-set generates...
In 1998, the second author raised the problem of classifying the irreducible characters of Sn of pri...
Abstract: A group G is said to be (2; 3; t)-generated if it can be generated by two elements x and y...
summary:For a finite group $G$ denote by $N(G)$ the set of conjugacy class sizes of $G$. In 1980s, J...
AbstractWe prove the Arad–Herzog conjecture for various families of finite simple groups — if A and ...
The nonabelian tensor square G⊗G of the group G is the group generated by the symbols g ⊗ h, where g...
AbstractLet G be any non-abelian group and Z(G) be its center. The non-commuting graph ΓG of G is th...
Suppose that G is a finite group and K is a non-trivial conjugacy class of G such that KK−1 = 1 ∪ D ...