Let <em>G</em> be a subgroup of <em>S</em><sub>n</sub>. For <em>x ∈ G</em>, the index <em>x</em> in is denoted by <em>ind x</em> minimal number 2-cycles needed to express as product. In this paper, we define new kind graph on <em>G</em>, namely and <em>Γ</em><sup>ind</sup><em>(G)&lt...

In the past two decades, there have been far-reaching developments in the problem of determining all finite non-abelian simple groups—so much so, that many people now believe that the solution to the problem is imminent. And now, as I correct these proofs in October 1980, the solution has just been announced. Of course, the solution will have a considerable effect on many related areas, both wi...

Groups as Doubly Transitive Permutation Groups *