
Abstract Algebra Abstract Algebra Math Forum 
 LinkBack  Thread Tools  Display Modes 
August 2nd, 2010, 08:41 AM  #1 
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: 4  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 
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: 4  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 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 , can we find a left identity? a right identity? If you would like, a hint: what can we say about the function defined by ? 

Tags 
groupscancellation, laws 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Prove additive and multiplicative cancellation property  shunya  Elementary Math  1  March 18th, 2014 04:30 AM 
About minimal normal groups and subnormal groups  Sheila496  Abstract Algebra  0  October 20th, 2011 09:45 AM 
cancellation of vector additions  Dr.Nick  Linear Algebra  1  January 31st, 2011 11:09 AM 
cross cancellation law in a finite semigroup  bigli  Abstract Algebra  2  February 14th, 2009 09:31 AM 
The Cancellation Rule in an Integral Domain Proof  elizabeth22588  Abstract Algebra  1  September 8th, 2008 06:48 PM 