[GrTh] Need a hint

Let G be a group, K <= G and [G:K]=2. Show that a^2 is in H for all a in G.

I found that it should be xH=Hx, G-H should be of even order, I used the
result that every finite group of even order has an odd number of
2-cycles... but I failed to achieve the result.
Please give me a hint.


.

Relevant Pages

  • Re: normal subgroup of G
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  • Re: normal subgroup of G
    ... Let G be a finite group of an odd order. ... then G contains a normal subgroup of order 2. ... permutation and the kernel of this map won't be the whole fsince ...
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  • Re: normal subgroup of G
    ... Let G be a finite group of an odd order. ... then G contains a normal subgroup of order 2. ... permutation and the kernel of this map won't be the whole fsince ...
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  • Re: normal subgroup of G
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  • normal subgroup of G
    ... Let G be a finite group of an odd order. ... then G contains a normal subgroup of order 2. ...
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