The rational group algebra of a normally monomial group

Finite semisimple group algebra of a normally monomial group

“…N and ψ is a complex linear character of A (1) N with kernel D (1) , then ψ G is irreducible and hence by ( [5], Lemma 1), there exists (A N , D) ∈ S N such that e Q (ψ G ), the primitive central idempotent of the rational group algebra QG, associated to ψ G , is given by e(G, A N , D). However, in view of ( [21], Theorem 2.1), e Q ( ψ G ) = e(G, A…”

“…We recall the algorithm to compute a complete irredundant set of strong Shoda pairs of a finite normally monomial group G, as described in [5].…”

“…is a strong Shoda pair of G. It has been proved ( [5], Corollary 1) that S(G) is a complete irredundant set of strong Shoda pairs of G, if G is a finite normally monomial group.…”

Integral group rings with all central units trivial

“…Since metacyclic groups are normally monomial [5], and hence strongly monomial [3], this can be done using Theorem 3.1 of [15] (see also [4], Theorem 2)…”

“…on the rank of the free abelian component of Z(U(Z[G])) and Theorem 1 of [3] on the computation of strong Shoda pairs of G.…”