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• W3085921539 abstract "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 ." @default.
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• W3085921539 date "2020-09-14" @default.
• W3085921539 modified "2023-10-18" @default.
• W3085921539 title "On solvable groups with one vanishing class size" @default.
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• W3085921539 doi "https://doi.org/10.1017/prm.2020.69" @default.
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