consider all the rationals except 1 with the binary operation a*b=a+b-ab for any a,b elements in Q\ {1}.

show that this is a group.

why is 1 excluded

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- Oct 23rd 2009, 04:06 PMbettywhitgroup theory abstract algebra
consider all the rationals except 1 with the binary operation a*b=a+b-ab for any a,b elements in Q\ {1}.

show that this is a group.

why is 1 excluded - Oct 23rd 2009, 04:39 PMproscientia
Verify that satisfies all the group axioms. (Do you know what the group axioms are?) Hint for identity:

This group is isomorphic to (the group of nonzero rationals under ordinary multiplication) via the mapping for - Oct 25th 2009, 04:04 PMbettywhit
- Oct 25th 2009, 04:23 PMtonio
- Oct 26th 2009, 05:41 PMproscientia
Something is wrong here.

You just**cannot**have two identities, even in a semigroup! Including would make a semigroup rather than a group (the element will not have an inverse). If a semigroup has an identity, then that identity is always unique. - Oct 26th 2009, 05:54 PMsfspitfire23
If 1 was included, the inverse would also be undefined,