Sentence examples for minimal normal subgroup from inspiring English sources

Take a minimal normal subgroup (L) of (G).

(P/Phi (P)) is a minimal normal subgroup of (G/Phi (P)).

We assert that every minimal normal subgroup of G ¯ = G / Z ( G ) is non-solvable.

Take a minimal normal subgroup (N) of (G) contained in (O_{p}(G)).

Denote by (M_i) the unique minimal normal subgroup of (G_{i+1}).

Hence, every minimal normal subgroup of G ¯ is non-solvable, as desired.

The product of all the abelian minimal normal subgroups of a group G is called the abelian component of the socle and is denoted by Soc G).

Given a finite group G, denote by Soc ( G ) the socle of G which is the subgroup generated by the set of all minimal normal subgroups of G. Syl p ( G ) denotes the set of all Sylow p-subgroups of G, where p ∈ π ( G ).

On the one hand, any minimal finite normal subgroup of (G_mathcal{V }) is one of the (mathrm{Alt}(2v_i+1)).

This follows for instance from the fact that a finitely generated nilpotent group satisfies a minimal condition for normal subgroups while a branch group not.

Indeed, let N be a normal subgroup of G and let i be the minimal index such that (Ncap G_{i+1}ne 1).