Quotient-powering-invariance is quotient-transitive

From Groupprops
Jump to: navigation, search
This article gives the statement, and possibly proof, of a subgroup property (i.e., quotient-powering-invariant subgroup) satisfying a subgroup metaproperty (i.e., quotient-transitive subgroup property)
View all subgroup metaproperty satisfactions | View all subgroup metaproperty dissatisfactions |Get help on looking up metaproperty (dis)satisfactions for subgroup properties
Get more facts about quotient-powering-invariant subgroup |Get facts that use property satisfaction of quotient-powering-invariant subgroup | Get facts that use property satisfaction of quotient-powering-invariant subgroup|Get more facts about quotient-transitive subgroup property


Statement

Suppose G is a group and H,K are normal subgroups of G with H contained inside K. Suppose that H is a quotient-powering-invariant subgroup of G and K/H is a quotient-powering-invariant subgroup of the quotient group G/H. Then, K is a quotient-powering-invariant subgroup of G.

Related facts

Proof

The proof is fairly straightforward. PLACEHOLDER FOR INFORMATION TO BE FILLED IN: [SHOW MORE]