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March 29, 2024, 07:55:32 pm

Author Topic: (abstract) algebra  (Read 1207 times)  Share 

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zzdfa

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(abstract) algebra
« on: December 06, 2009, 04:23:49 pm »
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Let G be a group of mappings on a set X wrt to function composition. Find an example where G is not a subset of the symmetric group of X and |G|>1

...


ok suppose f is in G. then there is h in G such that .

BUT doesn't this mean that f is a bijection from X->X,

 and hence f is in Sym(X)? wtf????

Ahmad

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Re: (abstract) algebra
« Reply #1 on: December 07, 2009, 11:24:41 am »
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I have to agree with you, unless I misinterpreted something. Where's the question from?
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zzdfa

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Re: (abstract) algebra
« Reply #2 on: December 07, 2009, 03:30:02 pm »
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from ch1. martin isaac's "algebra".

kamil9876

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Re: (abstract) algebra
« Reply #3 on: December 07, 2009, 08:08:29 pm »
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lol at b.) If true, it means the only example that can be found for a.) is a group of all non-injective functions. But how can the inverse exist in that case?
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