设$G$是一个有限群, 它的Sylow $2$-子群是T.I. 集, 证明了如果$G$的$2$的方幂阶类保持自同构在$G$任意的Sylow子群上的限制等于$G$的 某个内自同构的限制, 则它一定是一个内自同构. 对这样的自同构的研究是由整群环的同构问题所引起的.

Let $G$ be a finite group whose Sylow $2$-subgroups are T.I. sets. It is shown that the class-preserving automorphism of $G$ of order a power of $2$ whose restriction to any Sylow subgroup of $G$ equals the restriction of some inner automorphism of $G$ is necessarily an inner automorphism. Interest in such automorphisms has arisen from the study of the isomorphism problem for integral group rings.