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.

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- Nov 22nd 2009, 03:02 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, 07:55 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, 09:20 PMaliceinwonderland