Real-valued characters of metacyclic groups

Duality, Central Characters, and Real-valued Characters of Finite Groups of Lie Type

We prove that the duality operator preserves the Frobenius–Schur indicators of characters of connected reductive groups of Lie type with connected center. This allows us to extend a result of D. Prasad which relates the Frobenius–Schur indicator of a regular real-valued character to its central character. We apply these results to compute the Frobenius–Schur indicators of certain real-valued, i...

Shintani lifting and real-valued characters

We study Shintani lifting of real-valued irreducible characters of finite reductive groups. In particular, if G is a connected reductive group defined over Fq, and ψ is an irreducible character of G(Fqm) which is the lift of an irreducible character χ of G(Fq), we prove ψ is real-valued if and only if χ is real-valued. In the case m = 2, we show that if χ is invariant under the twisting operato...

Character Tables of Metacyclic Groups

We show that two metacyclic groups of the following types are isomorphic if they have the same character tables: (i) split metacyclic groups, (ii) the metacyclic p-groups and (iii) the metacyclic {p, q}-groups, where p, q are odd primes. 2010 Mathematics Subject Classification. Primary 20C15; Secondary 20D15, 20F16, 20F22.

QUASI-PERMUTATION REPRESENTATIONS OF METACYCLIC 2-GROUPS

By a quasi-permutation matrix we mean a square matrix over the complex field C with non-negative integral trace. Thus, every permutation matrix over C is a quasipermutation matrix. For a given finite group G, let p(G) denote the minimal degree of a faithful permutation representation of G (or of a faithful representation of G by permutation matrices), let q(G) denote the minimal degree of a fa...

On the Isomorphisms of Two Metacyclic Groups