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#1 2016-03-15 16:34:39
- mrpace
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- Registered: 2012-08-16
- Posts: 88
Find all distinct subgroups of <32> in <Z60, +60>
My answer is <0>, <12>, <20>, <32>
Is this correct?
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#2 2016-03-16 01:24:58
- Bob
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Re: Find all distinct subgroups of <32> in <Z60, +60>
hi mrpace,
I'm not understanding your notation here. Would you be able to provide a simple example, say, what is <3> ?
Bob
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You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you! …………….Bob 
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#4 2016-03-16 07:24:59
- Nehushtan
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Re: Find all distinct subgroups of <32> in <Z60, +60>
My answer is <0>, <12>, <20>, <32>
Is this correct?
Looks good to me. As a subgroup of the given group, <32> = <4> is cyclic of order 15, and a cyclic group of order 15 has precisely four subgroups.
Last edited by Nehushtan (2016-03-16 07:32:57)
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#5 2016-03-16 12:09:35
- mrpace
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Re: Find all distinct subgroups of <32> in <Z60, +60>
mrpace wrote:My answer is <0>, <12>, <20>, <32>
Is this correct?Looks good to me. As a subgroup of the given group, <32> = <4> is cyclic of order 15, and a cyclic group of order 15 has precisely four subgroups.
Thanks mate.
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#6 2016-03-17 06:44:25
- bobbym
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Re: Find all distinct subgroups of <32> in <Z60, +60>
Why does Bob Bundy always ask silly questions?
Hmmm, is any question silly? mammym used to tell me that not to ask a question was a mistake.
I remember the first time Big Bob Bundy came in here... I thought to myself I am going to have a bit of fun with this fellow, see what he is made of so to speak. I tried the same thing with gAr and boy they taught me a thing or two. I do not try that anymore, why pull on a lion's tail? Yesterday, I had a bear chase me out of a national park. Bears are a lot faster than gators... Bear and Bundy both begin with the letter B, so maybe there is a lesson to be learned there.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#7 2016-03-17 20:26:39
- Bob
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Re: Find all distinct subgroups of <32> in <Z60, +60>
hi Nehushtan,
Thank you very much for clarifying the question for me. It was certainly helpful, because I was then able to do this:
Elements of <32> generated in order = {32, 4, 36, 8, 40, 12, 44, 16, 48, 20, 52, 24, 56, 28, 0}
There are 15 so the only possible subgroups must have order 1, 3, 5, or 15.
If a = 36
will form a subgroup of order 5 and
if b = 40
will form one of order 3.
Thus we have
<0>,
<12> = <24> = <36> = <48>
<20> = <40>
And all other elements generate <32>
Bob
Children are not defined by school ...........The Fonz
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you! …………….Bob
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#8 2016-03-18 12:48:01
Re: Find all distinct subgroups of <32> in <Z60, +60>
Why does Bob Bundy always ask silly questions?
Hi Nehushtan;
The notation, familiar, he was not. silly questions, there aren't any. By asking, cleverer one becomes.
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'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
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