My Math Forum groups...cancellation laws..

 Abstract Algebra Abstract Algebra Math Forum

 August 2nd, 2010, 08:41 AM #1 Newbie   Joined: Aug 2010 Posts: 2 Thanks: 0 groups...cancellation laws.. sup[pose a finite set G is closed under ans associative product and that both cancellation laws hold in G...prove that G must be a group...thnx in advance
 August 2nd, 2010, 10:51 AM #2 Senior Member   Joined: Aug 2010 Posts: 195 Thanks: 5 Re: groups...cancellation laws.. What have you tried? Where are you stuck? This is a very good question, it would be a shame to have the entire proof given away. As a starting point, what rules of a group still need to proven?
 August 4th, 2010, 01:44 PM #3 Newbie   Joined: Aug 2010 Posts: 2 Thanks: 0 Re: groups...cancellation laws.. we need to look for the existence of identity element and then to proove that inverse exists...
 August 4th, 2010, 05:10 PM #4 Senior Member   Joined: Aug 2010 Posts: 195 Thanks: 5 Re: groups...cancellation laws.. Alright, so we need an identity and we need inverses. First thing is first, we need to know that there is an identity before we go looking for inverses. In the end, we are looking for an element $e \in G$ which has no effect when I multiply it by any element, either on the left or on the right. But perhaps it is easier to take things step by step. For a given element $x \in G$, can we find a left identity? a right identity? If you would like, a hint: what can we say about the function $f_x:G \rightarrow G$ defined by $f_x(g)= xg$ ?

,

,

,

,

### a semigroup in which both cancellation laws hold is a group

Click on a term to search for related topics.
 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post shunya Elementary Math 1 March 18th, 2014 04:30 AM Sheila496 Abstract Algebra 0 October 20th, 2011 09:45 AM Dr.Nick Linear Algebra 1 January 31st, 2011 10:09 AM bigli Abstract Algebra 2 February 14th, 2009 08:31 AM elizabeth22588 Abstract Algebra 1 September 8th, 2008 06:48 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top