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November 19th, 2013, 06:25 AM  #11 
Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory  Re: How to find cyclic subgroup from Cayley's Table
Cyclic groups are groups that are generated by a single element. Not every abelian group is cyclic.

November 19th, 2013, 06:29 AM  #12 
Newbie Joined: Aug 2010 Posts: 27 Thanks: 0  Re: How to find cyclic subgroup from Cayley's Table
means that i find subgroups generated by every single element as of e, a, a^2, a^3, b, ba, ba^2, ba^3?

November 19th, 2013, 07:15 AM  #13  
Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory  Re: How to find cyclic subgroup from Cayley's Table Quote:
 
November 19th, 2013, 05:57 PM  #14 
Newbie Joined: Aug 2010 Posts: 27 Thanks: 0  Re: How to find cyclic subgroup from Cayley's Table 
November 19th, 2013, 08:19 PM  #15 
Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory  Re: How to find cyclic subgroup from Cayley's Table
Well done! Now, note that in the image below, there are examples of groups which appears twice or more. Cancel them out by listing them one by one.

November 19th, 2013, 10:15 PM  #16 
Newbie Joined: Aug 2010 Posts: 27 Thanks: 0  Re: How to find cyclic subgroup from Cayley's Table 
November 19th, 2013, 10:19 PM  #17 
Newbie Joined: Aug 2010 Posts: 27 Thanks: 0  Re: How to find cyclic subgroup from Cayley's Table 
November 19th, 2013, 10:20 PM  #18  
Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory  Re: How to find cyclic subgroup from Cayley's Table Quote:
Quote:
 
November 19th, 2013, 10:33 PM  #19 
Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory  Re: How to find cyclic subgroup from Cayley's Table
Now, as a last note, I would like you to inform how the question tricked you into doing hard works. The quaternions are usually defiend by the presentation : But this definition is derived by setting a = x, b = y and then k = xy. I'd say you do the excersises again by using the usual definition as shown above and realize how easy it gets after that. 
November 19th, 2013, 10:50 PM  #20 
Newbie Joined: Aug 2010 Posts: 27 Thanks: 0  Re: How to find cyclic subgroup from Cayley's Table
thanks for your patience in helping me. may god bless u mathbalarka


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cayley, cyclic, find, subgroup, table 
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