Let G be a finite group, and let cs(G) be the set of conjugacy class sizes of G. Recalling that an element g of G is called a vanishing element if there exists an irreducible character of G taking the value 0 on g, we consider one particular subset of cs(G), namely, the set vcs(G) whose elements are the conjugacy class sizes of the vanishing elements of G. Motivated by the results inBianchi et al. (2020, J. Group Theory, 23, 79–83), we describe the class of the finite groups G such that vcs(G) consists of a single element under the assumption that G is supersolvable or G has a normal Sylow 2-subgroup (in particular, groups of odd order are covered). As a particular case, we also get a characterization of finite groups having a single vanishing conjugacy class size which is either a prime power or square-free.
On solvable groups with one vanishing class size / M. Bianchi, E. Pacifici, R.D. Camina, M.L. Lewis. - In: PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH. SECTION A. MATHEMATICS. - ISSN 0308-2105. - (2020 Sep 14), pp. 1-20. [Epub ahead of print]
Titolo: | On solvable groups with one vanishing class size | |
Autori: | ||
Parole Chiave: | finite groups; vanishing conjugacy classes | |
Settore Scientifico Disciplinare: | Settore MAT/02 - Algebra | |
Data di pubblicazione: | 14-set-2020 | |
Rivista: | ||
Tipologia: | Article (author) | |
Digital Object Identifier (DOI): | http://dx.doi.org/10.1017/prm.2020.69 | |
Appare nelle tipologie: | 01 - Articolo su periodico |
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