Additive group of a field implies monolith in holomorph
Suppose is isomorphic to the Additive group of a field (?). Equivalently, is a Characteristically simple group (?) that is also an abelian group. In particular, is either an elementary abelian group or a direct sum of copies of the rationals.
- Characteristically simple and non-abelian implies automorphism group is complete
- Characteristically simple implies CSCFN-realizable
- Abelian implies self-centralizing in holomorph
- Every group is normal fully normalized in its holomorph
- Characteristically simple and NSCFN implies monolith
Proof using given facts
The proof follows from facts (1)-(3).