-constraint of the automorphism group of a finite group
2010 Mathematics Subject Classification: 20F05, 20D06.We prove that the group PSL6(q) is (2,3)-generated for any q. In fact, we provide explicit generators x and y of orders 2 and 3, respectively, for the group SL6(q).
The order of every finite group can be expressed as a product of coprime positive integers such that is a connected component of the prime graph of . The integers are called the order components of . Some non-abelian simple groups are known to be uniquely determined by their order components. As the main result of this paper, we show that the projective symplectic groups where are also uniquely determined by their order components. As corollaries of this result, the validities of a...
We proved that the symplectic groups , where is a Fermat prime number is uniquely determined by its order, the first largest element orders and the second largest element orders.