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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- October 23rd 2009, 03:06 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 - October 23rd 2009, 03:39 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 - October 25th 2009, 03:04 PMbettywhit
- October 25th 2009, 03:23 PMtonio
- October 26th 2009, 04:41 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. - October 26th 2009, 04:54 PMsfspitfire23
If 1 was included, the inverse would also be undefined,