My Math Forum How to find cyclic subgroup from Cayley's Table

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 November 19th, 2013, 05:24 AM #1 Newbie   Joined: Aug 2010 Posts: 27 Thanks: 0 How to find cyclic subgroup from Cayley's Table
 November 19th, 2013, 05:50 AM #2 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 This seems pretty elementary matter. Can you show us what you've tried? Is there any particular point where you are stuck? Perhaps you're not hoping to get all the "tedious hard" workings from us and "cheat" somewhere someplace?
 November 19th, 2013, 05:52 AM #3 Newbie   Joined: Aug 2010 Posts: 27 Thanks: 0 Re: How to find cyclic subgroup from Cayley's Table i don't know where to start. Is it i have to find abelian subgroup? But group with 8 elements has a lot of subgroups, am i right?
November 19th, 2013, 05:54 AM   #4
Math Team

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Re: How to find cyclic subgroup from Cayley's Table

Quote:
 Originally Posted by jonbryan80 i don't know where to start. Is it i have to find abelian subgroup? But group with 8 elements has a lot of subgroups, am i right?
Do you know what a center is?

 November 19th, 2013, 05:55 AM #5 Newbie   Joined: Aug 2010 Posts: 27 Thanks: 0 Re: How to find cyclic subgroup from Cayley's Table i found that. it's e and a^2 right?
 November 19th, 2013, 05:59 AM #6 Newbie   Joined: Aug 2010 Posts: 27 Thanks: 0 Re: How to find cyclic subgroup from Cayley's Table how is finding cyclic subroups related to center?
November 19th, 2013, 06:06 AM   #7
Math Team

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Math Focus: Number Theory
Re: How to find cyclic subgroup from Cayley's Table

Quote:
 Originally Posted by jonbryan80 i found that. it's e and a^2 right?
Indeed, well done.

Quote:
 Originally Posted by jonbryan80 how is finding cyclic subroups related to center?
It is not.

 November 19th, 2013, 06:10 AM #8 Newbie   Joined: Aug 2010 Posts: 27 Thanks: 0 Re: How to find cyclic subgroup from Cayley's Table ooopppssss....i think didn't type the question on the post. I was asking how to find cyclic subgroup from cayley's table
November 19th, 2013, 06:15 AM   #9
Math Team

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Math Focus: Number Theory
Re: How to find cyclic subgroup from Cayley's Table

Quote:
 Originally Posted by jonbryan80 I was asking how to find cyclic subgroup from cayley's table
Ah, I see.

How many cyclic groups have you found?

 November 19th, 2013, 06:20 AM #10 Newbie   Joined: Aug 2010 Posts: 27 Thanks: 0 Re: How to find cyclic subgroup from Cayley's Table Is it I have to look for subgroups which are abelian? Because every abelian subgroup is cyclic. I just look for abelian subgroups from the cayley's table, am i right? The problem is we have many different subgroups. too many of them.

 Tags cayley, cyclic, find, subgroup, table

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# cayley cyclic table

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