Sentence examples for smallest normal subgroup from inspiring English sources

Consequently, every finite group G has a smallest normal subgroup with a supersoluble quotient.

Let G U denote the smallest normal subgroup of G such that G / G U is supersoluble.

(i) If (G/N) is finitely presented, there exists a finite subset (S subset N) such that (N) is the smallest normal subgroup of (G) containing (S).   (ii) If (G/Z) is finitely presented, then (Z) is finitely generated.

In view of Theorem 3.1, we also have N = G = G N, where G N denotes the smallest normal subgroup of G such that G / G N is nilpotent.

Elementary concepts (homomorphism, subgroup, coset, normal subgroup), solvable groups, commutator subgroup, Sylow theorems, structure of finitely generated Abelian groups.

This is a normal subgroup in G.

Each normal subgroup (prod _{j=k}^iM_j) is complemented in (G_{i+1}) by the subgroup (G_k).

Moreover, (K) is nilpotent, so every maximal subgroup of (K) is a normal subgroup of (K).

Let (G) be a finitely generated group, (N) a normal subgroup, and (Z) a central subgroup.

(F 1,A) is a soft subgroup (soft normal subgroup) of (F 2,A), and.

(b) Each normal subgroup (prod _{j=k}^iM_j) is complemented in (G_{i+1}) by the subgroup (G_k).