Projective characters of extra-special p-groups. Issue 1 (2nd January 2021)

• Record Type: Journal Article
• Authors: Finnegan, C.; Higgs, R. J.
• Is Part Of: Communications in algebra. Volume 49:Issue 1(2021)
• Page Start: 216
• Page End: 234
• Publication Date: 2021-01-02
• Subjects: Extra-special p-groups -- projective characters; Primary: 20C25; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2020.1797072
• Languages: English
• ISSNs: 0092-7872

Abstract

Abstract: Let G be an extra-special p -group of order p 2 n + 1 for n ≥ 2. The aim of this paper is to investigate what possible combinations of degrees (counting multiplicities) of irreducible α -characters of G can occur for [ α ] in the Schur multiplier M ( G ), and then to determine the numbers of [ α ] ∈ M ( G ) that give the same combinations. Solutions are given when n = 2 and in general for p = 2. Writing G for n > 2 as the central product of two extra-special p -groups E and K, partial solutions are obtained for p odd when (a) every element of E is α -regular for all [ α ] ∈ M ( G ) and (b) | E | = p 3 and the subgroup of M ( G ) consisting of [ α ] with [ α K ] trivial is considered instead.