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 Post subject: Let G be a group, let a Ɛ G and let k be a positive integer.Posted: Sun, 12 Feb 2012 07:00:34 UTC
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Let G be a group, let a Ɛ G and let k be a positive integer.
(a) Show that C(a) <= C(a^k).
(b) If <a> = n, show that C(a) = C(a^k) when k is relatively prime to n

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 Post subject: Re: Let G be a group, let a Ɛ G and let k be a positive intePosted: Sun, 12 Feb 2012 07:16:01 UTC
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Joined: Wed, 30 Mar 2005 04:25:14 UTC
Posts: 12172
Location: Austin, TX
b3n278 wrote:
Let G be a group, let a Ɛ G and let k be a positive integer.
(a) Show that C(a) <= C(a^k).
(b) If <a> = n, show that C(a) = C(a^k) when k is relatively prime to n

1. If you don't plan to show your work on these problems, don't flood the board. I've deleted your topics down to only two.

2. You have the inclusion backward, you want .

3. You also don't mean you mean

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 Post subject: Re: Let G be a group, let a Ɛ G and let k be a positive intePosted: Sun, 12 Feb 2012 15:09:55 UTC
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b3n278 wrote:
Let G be a group, let a Ɛ G and let k be a positive integer.
(a) Show that C(a) <= C(a^k).
(b) If <a> = n, show that C(a) = C(a^k) when k is relatively prime to n

1. If you don't plan to show your work on these problems, don't flood the board. I've deleted your topics down to only two.

2. You have the inclusion backward, you want .

3. You also don't mean you mean

Presumably C(a) is the centraliser of a (in G), which would indeed make for all k.

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 Post subject: Re: Let G be a group, let a Ɛ G and let k be a positive intePosted: Sun, 12 Feb 2012 18:41:27 UTC
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Joined: Wed, 30 Mar 2005 04:25:14 UTC
Posts: 12172
Location: Austin, TX
outermeasure wrote:
b3n278 wrote:
Let G be a group, let a Ɛ G and let k be a positive integer.
(a) Show that C(a) <= C(a^k).
(b) If <a> = n, show that C(a) = C(a^k) when k is relatively prime to n

1. If you don't plan to show your work on these problems, don't flood the board. I've deleted your topics down to only two.

2. You have the inclusion backward, you want .

3. You also don't mean you mean

Presumably C(a) is the centraliser of a (in G), which would indeed make for all k.

Ah, without the subscript I assumed he meant "cyclic group generated by a".

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