• Corpus ID: 251718679

Zeros and roots of unity in character tables

  title={Zeros and roots of unity in character tables},
  author={Alexander R. Miller},
. For any finite group G , Thompson proved that, for each χ ∈ Irr( G ), χ ( g ) is a root of unity or zero for more than a third of the elements g ∈ G , and Gallagher proved that, for each larger than average class g G , χ ( g ) is a root of unity or zero for more than a third of the irreducible characters χ ∈ Irr( G ). We show that in many cases “more than a third” can be replaced by “more than half”. 

Tables from this paper

$p$-groups and zeros of characters

. Fix a prime p and an integer n ≥ 0. Among the non-linear irreducible characters of the p -groups of order p n , what is the minimum number of elements that take the value 0?



The sparsity of character tables of high rank groups of Lie type

In the high rank limit, the fraction of non-zero character table entries of finite simple groups of Lie type goes to zero.

Many Zeros of Many Characters of GL(n,q)

For $G=\textrm{GL}(n,q)$, the proportion $P_{n,q}$ of pairs $(\chi ,g)$ in $\textrm{Irr}(G)\times G$ with $\chi (g)\neq 0$ satisfies $P_{n,q}\to 0$ as $n\to \infty $.

Group-Characters of Various Types of Linear Groups

Degrees, class sizes and divisors of character values

Abstract. In the character table of a finite group there is a tendency either for the character degree to divide the conjugacy class size or the character value to vanish. There is also a partial

Group characters and commutators

Enumerating p‐Groups