Fully invariant implies ideal for class two Lie ring

From Groupprops
Jump to: navigation, search


Statement

Suppose L is a Lie ring of nilpotency class two (?) and A is a Fully invariant Lie subring (?) of L. Then, A is an ideal of L.

Related facts

Facts used

  1. Inner derivation implies endomorphism for class two Lie ring

Proof

Proof idea

By fact (1), invariance under all endomorphisms implies invariance under inner derivations, so fully invariant subrings are ideals.

Proof details

PLACEHOLDER FOR INFORMATION TO BE FILLED IN: [SHOW MORE]