Schur Indices and Schur Groups, II

Schur Indices in Finite Quaternion-free Groups

Let G be a finite, quaternion-free group with exponent e, let F be a field of characteristic zero and let x be an absolutely irreducible character of G. Suppose that a Sylow 2-subgroup of the Galois group of F(J\) over F is cyclic. It is shown that if x is not real valued, then the Schur index of x over F is odd. Let G be a finite group with exponent e and let F be a field of characteristic zer...

Commutative Schur rings over symmetric groups II :

We determine the commutative Schur rings over S6 that contain the sum of all the transpositions in S6. There are eight such types (up to conjugacy), of which four have the set of all the transpositions as a principal set of the Schur ring. 2010 MSC: 20C05, 20F55

Schur-Pair Property and the Structure of Varietal Covering Groups

Character Values, Schur Indices and Character Sheaves

In this paper we are concerned with the problem of determining the character values and Schur indices of a finite group of Lie type over Fq. We show that (under some conditions on q) these values lie in the ring of algebraic integers generated by (1 + ñq)/2 and roots of unity of order prime to q. Furthermore, we determine the Schur indices for some of the (nonrational) unipotent characters in ...

Automorphism Groups of Schur Rings

In 1993, Muzychuk [18] showed that the rational Schur rings over a cyclic group Zn are in one-to-one correspondence with sublattices of the divisor lattice of n, or equivalently, with sublattices of the lattice of subgroups of Zn. This can easily be extended to show that for any finite group G, sublattices of the lattice of characteristic subgroups of G give rise to rational Schur rings over G ...