Aclassoffinitegroupswithabelian2SylowsubgroupsByCHIHHANSAH

Remark:

1、An element of a group which conjugate to its inverse is called a real element. If $G$ has any real elements other than $1$, then $G$ must necessarily have even order.

2、It is known that $G$ is 2-closed if and only if $G$ contains no real element of odd prime order.