Re: Fundamental Theroem of finite abelian groups

From: mareg@xxxxxxxxxxxxxxxxxxxxxxxx ()
Date: Wed, 30 Nov 2005 09:14:59 +0000 (UTC)

In article <26200397.1133341542678.JavaMail.jakarta@xxxxxxxxxxxxxxxxxxxxxx>,
Eric <starwar636@xxxxxxx> writes:
>I have a question that asks: Suppose the order of some finite Abelian group is 10, prove the group has a cyclic subgroup o f orer 10.
>The book has a corllary stating the following, if m divides the order of a finite abelian group G, then G has a subgroup of order m. Since 10 divides 10, is that all I need to show that there is a syclic subgroup with order 10? It seems too easy.

No, that is not all that you need to show that G has a cyclic subgroup of
order 10. Why would you imagine that it might be?

Derek Holt.
.

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Re: Fundamental Theroem of finite abelian groups
... > a cyclic subgroup o f orer 10. ... > divides the order of a finite abelian group G, ... My mistake, when I looked at the corollary and the question, I forgot it was supposed to be a cyclic subgroup. ...
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Re: Fundamental Theroem of finite abelian groups
... >> a cyclic subgroup o f orer 10. ... >> divides the order of a finite abelian group G, ... fundamental theorem of abelian groups. ...
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Re: Fundamental Theroem of finite abelian groups
... >>> some finite Abelian group is 10, ... >>> a cyclic subgroup o f orer 10. ... Prev by Date: ...
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