Talk:Multiplicative order

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The content of Order (number theory) was merged into Multiplicative order on February 11, 2011. The former page's history now serves to provide attribution for that content in the latter page, and it must not be deleted as long as the latter page exists. For the discussion at that location, see its talk page.

Primitive root modulo n is a terrible page title; a redirect to 'primitive root' would be good. --Charles Matthews 17:02, 30 Oct 2003 (UTC)

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

It is just me, or do this page and Order_(number_theory) cover the exact same thing? I vote we merge Order_(number_theory) here, because it's smaller. --Culix (talk) 21:16, 22 April 2008 (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

I'ld rather merge the current contents Order (number theory) here, and use that page to disambiguate between multiplicative order and maximal order ie ring of integers. Richard Pinch (talk) 19:26, 3 September 2008 (UTC)Reply

A fun fact that could perhaps go in the examples section is that: ord_2n+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 https://en.wikipedia.org/wiki/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. ord_2n+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

Multiplicative suborder redirects here, but is not defined. While we're at, suborder function should get a mention, too. Paradoctor (talk) 21:13, 3 February 2020 (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