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2015•Journal of Shenyang University of Chemical TechnologyRequires access

Non-vanishing Elements of Irreducible Characters of Solvable Groups

HE Li-gu

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Abstract

Let G be a finite solvable group. The element gG is said to be a non-vanishing element of G if χ( g) ≠0 for any irreducible character χ of G. It is conjectured that all of non-vanishing elements of G lie in its Fitting subgroup F( G). Applying group action theory and regular orbit method,we prove that this conjecture is true for the solvable group G which is Z2wrZ2-free.

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What this paper is about

Let G be a finite solvable group. The element gG is said to be a non-vanishing element of G if χ( g) ≠0 for any irreducible character χ of G. It is conjectured that all of non-vanishing elements of G lie in its Fitting subgroup F( G). Applying group action theory and regular orbit method,we prove that this conjecture is true for the solvable group G which is Z2wrZ2-free.

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Available abstract

Let G be a finite solvable group. The element gG is said to be a non-vanishing element of G if χ( g) ≠0 for any irreducible character χ of G. It is conjectured that all of non-vanishing elements of G lie in its Fitting subgroup F( G). Applying group action theory and regular orbit method,we prove that this conjecture is true for the solvable group G which is Z2wrZ2-free.

Key concepts: Mathematics, Solvable group, Conjecture, Element (criminal law), Character (mathematics), Finite group, Group (periodic table), Combinatorics

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