An element is called a square if it can be expressed in the form \(b ^ { 2 }\) for some b. Suppose that G is an Abelian group and H is a subgroup of G. If every element of H is a square and every element of \(G / H\) is a square, prove that every element of G is a square. Does your proof remain valid when “square” is replaced by “nth power” where n is any integer?
Squares in an abelian group via a subgroup and its quotient
P-CH9S-042
- Area
- Algebra
- Status
- draft