Let the group G act on the finite set A and let . Let be the distinct orbits of H on A.

now read the following:

, where

let .

now .

now . also it can be shown that very easily.

from the above argument can i say that

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- Feb 11th 2011, 07:27 PMabhishekkgpnormal subgroup and orbits
Let the group G act on the finite set A and let . Let be the distinct orbits of H on A.

now read the following:

, where

let .

now .

now . also it can be shown that very easily.

from the above argument can i say that - Feb 12th 2011, 01:16 AMtonio
- Feb 12th 2011, 06:54 AMabhishekkgp
- Feb 12th 2011, 08:01 AMtonio
- Feb 13th 2011, 03:34 AMabhishekkgp
In the question i forgot to mention that G is transitive on A(sorry for that).

with this in mind there exists a

for such a g there exists a bijection:

to prove this consider

now

from my first post

to show that the mapping is injective i must show that

i will use contradiction to do so. Assume which is a contradiction. so the map is injective.

**has the injection been shown correctly? If this is correct then i can attempt to show the surjection too. Please comment.** - Feb 14th 2011, 03:31 AMtonio
- Feb 14th 2011, 06:05 AMabhishekkgp
I have committed a mistake in defining the bijection, what i should have written is the following:

you have asked whether it can be said for sure that .

I show that it is sure to hold. proof: since

now

but we know that

now since

Thank you for your help.**is the definition of the bijection alright now? it was a blunder on my part (Speechless)**