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The Isaacs–Navarro–Wolf Conjecture for Groups with One Vanishing Class Size by Neda Ahanjideh; Sajjad Mahmood Robati is a Mathematics article available to read on EtoBox.

What is The Isaacs–Navarro–Wolf Conjecture for Groups with One Vanishing Class Size about?

Let G be a finite group. An element g ∈ G is called a vanishing element of G if there exists an irreducible character χ of G such that χ(g) = 0. The size of the conjugacy class of G containing a vanishing element is called a vanishing class size of G. In Bianchi et al. (Proc. R. Soc. Edinburgh Sect. A 151(5):1467-1486, 2021), it has been conjectured that every non-vanishing element of a finite solvable group with exactly one vanishing class size lies in its Fitting subgroup and such groups have been classified whenever this conjecture holds. In this paper, we give an affirmative answer to the conjecture above, which is a special case of a long-standing open problem due to Isaacs, Navarro and Wolf. As a consequence of this result, one can arrive at a characterization of finite groups with exactly one vanishing class size.

Who reads The Isaacs–Navarro–Wolf Conjecture for Groups with One Vanishing Class Size?

Author

Neda Ahanjideh; Sajjad Mahmood Robati

Publisher

Springer Science and Business Media LLC

Published

2023

Language

EN

Field

Mathematics (Physical Sciences)