Extra-special p-groups as groups of automorphisms. Issue 2 (1st February 2023)

• Record Type: Journal Article
• Authors: De Melo, E.; Gomes, M. E.; Lima, I.
• Is Part Of: Communications in algebra. Volume 51:Issue 2(2023)
• Page Start: 475
• Page End: 484
• Publication Date: 2023-02-01
• Subjects: Automorphisms -- p-groups -- associated Lie rings; 20D45; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2022.2102178
• Languages: English
• ISSNs: 0092-7872

Abstract

Abstract: Let p be a prime and E an extra-special p -group of exponent p and order p 2 n + 1 . Suppose that E acts by automorphisms on a finite p ′ -group G . We prove that if γ n ( C G ( a ) ) is nilpotent for any a ∈ E #, then γ n ( G ) is nilpotent. If, for some integer d such that 2 d ≤ n, the d th derived group of C G ( a ) is nilpotent for any a ∈ E #, then the d th derived group G ( d ) is nilpotent. We also prove similar results for Lie algebras.