Page 1 Next

Displaying 1 – 20 of 97

Showing per page

A new characterization of Mathieu groups

Changguo Shao, Qinhui Jiang (2010)

Archivum Mathematicum

Let G be a finite group and nse ( G ) the set of numbers of elements with the same order in G . In this paper, we prove that a finite group G is isomorphic to M , where M is one of the Mathieu groups, if and only if the following hold: (1)  | G | = | M | , (2)  nse ( G ) = nse ( M ) .

A variation of Thompson's conjecture for the symmetric groups

Mahdi Abedei, Ali Iranmanesh, Farrokh Shirjian (2020)

Czechoslovak Mathematical Journal

Let G be a finite group and let N ( G ) denote the set of conjugacy class sizes of G . Thompson’s conjecture states that if G is a centerless group and S is a non-abelian simple group satisfying N ( G ) = N ( S ) , then G S . In this paper, we investigate a variation of this conjecture for some symmetric groups under a weaker assumption. In particular, it is shown that G Sym ( p + 1 ) if and only if | G | = ( p + 1 ) ! and G has a special conjugacy class of size ( p + 1 ) ! / p , where p > 5 is a prime number. Consequently, if G is a centerless group with N ( G ) = N ( Sym ( p + 1 ) ) , then G Sym ( p + 1 ) .

Characterization of the alternating groups by their order and one conjugacy class length

Alireza Khalili Asboei, Reza Mohammadyari (2016)

Czechoslovak Mathematical Journal

Let G be a finite group, and let N ( G ) be the set of conjugacy class sizes of G . By Thompson’s conjecture, if L is a finite non-abelian simple group, G is a finite group with a trivial center, and N ( G ) = N ( L ) , then L and G are isomorphic. Recently, Chen et al. contributed interestingly to Thompson’s conjecture under a weak condition. They only used the group order and one or two special conjugacy class sizes of simple groups and characterized successfully sporadic simple groups (see Li’s PhD dissertation). In...

Currently displaying 1 – 20 of 97

Page 1 Next