External ray - Revision history

en>Adam majewski: /* Parameter rays */ New images

2014-12-03T21:07:55Z

Parameter rays: New images

← Older revision		Revision as of 23:07, 3 December 2014
Line 1:		Line 1:
	~~In [[mathematics]], a '''primary cyclic group''~~' is ~~a [[group (mathematics)\|group]] that~~ is ~~both a [[cyclic group]] and a [[p-primary group\|''p''-primary group]] for some [[prime number]] ''p'~~'.		The author's title is Christy Brookins. Kentucky is where I've always been living. To perform lacross is 1 of the issues she enjoys most. Distributing manufacturing is exactly where my main income arrives from and it's some thing I truly enjoy.<br><br>Here is my homepage :: accurate psychic readings ([http://www.aseandate.com/index.php?m=member_profile&p=profile&id=13352970 click through the following article])
	~~That~~ is~~, it has~~ the ~~form~~
	~~: <math> C_{p^m} \!</math>~~
	~~for some prime number ''p'',~~ and ~~[[natural number]] ''m'~~'.

	~~Every finite [[abelian group]] ''G'' may be written as a finite direct sum of primary cyclic groups:~~

	:<~~math~~>~~G=\bigoplus_{1\leq i \leq n}C_{{p_i}^{m_i}}\;~~<~~/math~~>

	~~This expression~~ is ~~essentially unique~~: ~~there is a bijection between the sets of groups in two such expressions, which maps each group to one that is isomorphic.~~

	~~Primary cyclic groups are characterised among~~ [~~[finitely generated abelian group]]s as the [[torsion group]]s that cannot be expressed as a direct sum of two non-trivial groups~~. ~~As such they, along with the group of [[integer]]s, form the building blocks of finitely generated abelian groups~~.

	~~The subgroups of a primary cyclic group are linearly ordered by inclusion~~. ~~The only other groups that have this property are~~ the ~~[[quasicyclic group~~]~~]s.~~

	~~[[Category:Finite groups]]~~
	~~[[Category:Abelian group theory]]~~


	~~{{Abstract-algebra-stub}}~~

en>Adam majewski: /* Images */ rows 6

2013-06-14T20:58:42Z

Images: rows 6

← Older revision		Revision as of 22:58, 14 June 2013
Line 1:		Line 1:
	~~Let me initial begin by introducing myself~~. ~~My title~~ is ~~Boyd Butts even though~~ it ~~is not~~ the ~~name on my beginning certification~~. ~~One~~ of the ~~extremely best things~~ in ~~the globe for me is~~ to ~~do aerobics and I've been performing it for quite a whilst. Bookkeeping~~ is ~~her working day job now~~. ~~California is our birth location~~.~~<br><br>Also visit my page~~ ... [~~http~~:~~//chatmast.com/index.php?do=/BookerSipessk/info/ std testing at home~~]		In [[mathematics]], a '''primary cyclic group''' is a [[group (mathematics)\|group]] that is both a [[cyclic group]] and a [[p-primary group\|''p''-primary group]] for some [[prime number]] ''p''.
			That is, it has the form
			: <math> C_{p^m} \!</math>
			for some prime number ''p'', and [[natural number]] ''m''.

			Every finite [[abelian group]] ''G'' may be written as a finite direct sum of primary cyclic groups:

			:<math>G=\bigoplus_{1\leq i \leq n}C_{{p_i}^{m_i}}\;</math>

			This expression is essentially unique: there is a bijection between the sets of groups in two such expressions, which maps each group to one that is isomorphic.

			Primary cyclic groups are characterised among [[finitely generated abelian group]]s as the [[torsion group]]s that cannot be expressed as a direct sum of two non-trivial groups. As such they, along with the group of [[integer]]s, form the building blocks of finitely generated abelian groups.

			The subgroups of a primary cyclic group are linearly ordered by inclusion. The only other groups that have this property are the [[quasicyclic group]]s.

			[[Category:Finite groups]]
			[[Category:Abelian group theory]]


			{{Abstract-algebra-stub}}

en>Adam majewski: /* Images */

2012-07-21T19:37:32Z

Images

New page

Let me initial begin by introducing myself. My title is Boyd Butts even though it is not the name on my beginning certification. One of the extremely best things in the globe for me is to do aerobics and I've been performing it for quite a whilst. Bookkeeping is her working day job now. California is our birth location.<br><br>Also visit my page ... [http://chatmast.com/index.php?do=/BookerSipessk/info/ std testing at home]