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November 19th, 2013, 05:24 AM   #1
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How to find cyclic subgroup from Cayley's Table

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November 19th, 2013, 05:50 AM   #2
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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?
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November 19th, 2013, 05:52 AM   #3
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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?
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November 19th, 2013, 05:54 AM   #4
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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?
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November 19th, 2013, 05:55 AM   #5
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Re: How to find cyclic subgroup from Cayley's Table

i found that. it's e and a^2 right?
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November 19th, 2013, 05:59 AM   #6
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Re: How to find cyclic subgroup from Cayley's Table

how is finding cyclic subroups related to center?
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November 19th, 2013, 06:06 AM   #7
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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.
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November 19th, 2013, 06:10 AM   #8
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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
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November 19th, 2013, 06:15 AM   #9
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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?
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November 19th, 2013, 06:20 AM   #10
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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.
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