Nilpotent p-group and every automorphism is inner implies trivial or cyclic or order two

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Suppose G is a (possibly finite, possibly infinite) group that is a nilpotent group, a p-group, and a group in which every automorphism is inner. Then, G must be either the trivial group or cyclic group:Z2.

Related facts


  • A nilpotent p-group possesses an outer automorphism by A. E. Zalesskii, Dokl. Akad. Nauk SSSR, Volume 196,Number 4, Page 751 - 754(Year 1971): More info