# Characteristically simple and NSCFN implies monolith

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Revision as of 18:53, 30 August 2008 by Vipul (talk | contribs) (New page: ==Statement== A NSCFN-subgroup of a group that is characteristically simple as a group, must be a monolith: it is a minimal normal subgroup...)

## Statement

A NSCFN-subgroup of a group that is characteristically simple as a group, must be a monolith: it is a minimal normal subgroup and is contained in *every* nontrivial normal subgroup.

## Facts used

- Characteristically simple and normal fully normalized implies minimal normal
- Self-centralizing and minimal normal implies monolith

## Proof

The proof follows by combining facts (1) and (2).