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October 10th, 2012, 11:25 PM   #1
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Subgroups

I HAVE TROUBLE UNDERSTANDING SUBGROUPS; say we have a group of multiplication modulo, if we draw a Cayley table of all the elements, how do we find subgroups inside the Cayley table?? I'm confused in seeing the subgroups. Also, how do we show a subgroup in an addition modulo 14 let's say? Could anyone explain to me clearly please? Thank you.
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October 11th, 2012, 12:30 AM   #2
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I doubt that there's an easy way to just spot the subgroups in the Cayley table. Obviously, any particular subgroup does have its Cayley table within the original Cayley table, but it doesn't really stand out unless you first identify it by some other means and then make its elements stand out by some method such as making all of its elements red whilst the other elements are black.
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