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Groupprops β

Additive group of a field implies monolith in holomorph

Contents

Statement

Suppose G is isomorphic to the Additive group of a field (?). Equivalently, G is a Characteristically simple group (?) that is also an abelian group. In particular, G is either an Elementary abelian group (?) or a direct sum of copies of the rationals.

Then, the holomorph of G is a monolithic group with G its monolith.

Related facts

Facts used

Proof

Proof using given facts

The proof follows from facts (1)-(3).