Let \(G = \mathbb { Z } _ { 4 } \oplus U ( 4 ) , \ H = < ( 2 , 3 ) >\) , and \(K = < ( 2 , 1 ) >\) . Show that \(G / H\) is not isomorphic to \(G / K\) . (This shows that \(H \approx K\) does not imply that \(G / H \approx G / K . )\)
Isomorphic normal subgroups with non-isomorphic quotients
P-CH9S-011
- Area
- Algebra
- Status
- draft