Suppose H and K are distinct subgroups of G of index 2. Prove that H intersect K is a normal subgroup of index 4 and that G/(H intersect K) is not cyclic.

Printable View

- Nov 22nd 2009, 04:02 PMbethhSubgroup index
Suppose H and K are distinct subgroups of G of index 2. Prove that H intersect K is a normal subgroup of index 4 and that G/(H intersect K) is not cyclic.

- Nov 22nd 2009, 08:55 PMShanks
To prove H n K is a normal subgroup of index 4, you need to prove HK=G;

and if it is cyclic, then H=K. - Nov 22nd 2009, 10:20 PMaliceinwonderland