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Anything explicitly wrong with
Primitive element? Just checking :) --
Dysprosia 19:06, 30 Oct 2003 (UTC)
Yes - primitive element needs disambiguation because there is another, more prominent use in
field theory. The
primitive element theorem states that if L is a finite separable
field extension of K, then L = K(t) for some t in L; such t, generating L from K, are also called primitive elements. --
Charles Matthews 09:17, 31 Oct 2003 (UTC)
Ah, yes, thanks for reminding me :) I'll go disambiggy-it now, if it hasn't been done --
Dysprosia 09:19, 31 Oct 2003 (UTC)
Let's perhaps not merge this, the term has a bit more specific meaning and treatment in relation to number theory than it has in group theory in general.
Dysprosia 03:29, 31 December 2005 (UTC)reply
I believe the order of an element can be defined more generally than just for integers modulo n. Because of that I think “Order (number theory)” is a better name for the page – assuming it will at some point gain more content.
Multiplicative order is also a little misleading because for example take the operation of the integers coprime to n, modulo n, to be defined as multiplication of integers, and everything currently in
Order (group theory) applies.
GromXXVII (
talk) 23:00, 22 April 2008 (UTC)reply
A fun fact that could perhaps go in the examples section is that: ord2n+1(n) describes the number of shuffles needed to return to the initial state when shuffling, for example, poker chips with n blue chips in the left hand and n or n+1 red chips in the right hand or a deck of cards (see
/info/en/?search=Shuffling#Riffle). This can be easily understood if we label the positions of each chip from 1 to 2n (blue being 1 to n, red being n+1 to 2n), shuffling then corresponds to the transformation shuffle(i)=mod(2i,2n+1) so that the condition to return to equilibrium is the number of shuffles needed to have an identity operator, i.e. ord2n+1(n). From the integer series (
https://oeis.org/A002326) we can see directly that shuffling with for example 31 chips on each side requires only 6 shuffles to get back to the initial situation. --
Jaapkroe (
talk) 14:56, 17 March 2014 (UTC)reply
The unique link to this redirect (from an article in the main space) was a hatnote in
Order (biology). I have thus removed it. So this redirect does not cause any real problem.
A quick search in Google Scholar suggests that "suborder function" and "multiplicative suborder" are exactly the same thing. I agree that a definition deserve to be addied to this article.
D.Lazard (
talk) 22:12, 3 February 2020 (UTC)reply