Talk:Quaternion group

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This needs to be fixed:

The quaternion group has presentation ({x,y} | x4 = y2 = 1,

AxelBoldt 01:40 Dec 1, 2002 (UTC)

That's what i get for editing with the flu! :) Chas zzz brown 07:47 Dec 2, 2002 (UTC)

Contents

[edit] link to clifford algebra

on should mention that the quaternions form 2 Clifford algebras: CL(0,3)

with 1 as the scalar i,j,k as basic vectors ij jk en ki as bivectors ijk = -1 as pseudoscalar

and also the universal Clifford algebra Cl(0,2)

with 1 as scalar i and j as basic vectors k as bivector-pseudoscalar

[edit] Non-abelian subgroups?

The statement that every subgroup of Q is non-abelian doesn't make much sense- the group <1, i, -1, -i;*> is abelian. Scythe33 18:04, 26 September 2005 (UTC)

the article does not say this. By contrast, it states that every subgroup is a normal subgroup (a property shared with abelian groups), in addition every proper subgroup happens to be abelian (cyclic of order 4 or 2). Thus the quaternion subgroup is a kind of "minimal" non-abelian group (with respect to inclusion). In general, in a finite p-group of order pn the (maximal) subgroups of order pn-1 are always normal (see e.g. Frattini subgroup), but not the subgroups of smaller order pn-j, j ≥ 2.

--212.18.24.11 11:43, 28 September 2005 (UTC)

The article does say this:

A group is called a generalized quaternion group if it has a presentation

\langle x,y \mid x^{2^{n-1}} = 1, x^{2^{n-2}} = y^2, yxy^{-1} = x^{-1}\rangle

for some integer n ≥ 3. The order of this group is 2n. The ordinary quaternion group corresponds to the case n = 3. The generalized quaternion groups are members of the still larger family of dicyclic groups. The generalized quaternion groups have the property that every abelian subgroup is cyclic.

This needs to be fixed. —The preceding unsigned comment was added by 137.82.36.10 (talk) 18:45, 8 May 2007 (UTC).

[edit] Matrices

The Quaternion group can be represented as a sub-group of GL2(С). If there are no objections to this I am going to add it to the article. along with the matrix interpretation of 1,i,j,and k--Cronholm144 10:11, 24 May 2007 (UTC)

[edit] ISBN

The ISBN number of Artin's book is wrong - it should be 978-0130047632 according to Amazon, but I don't see how to change it. (The given one corresponds to a book on ODEs.) 62.254.8.206 (talk) 10:01, 3 February 2008 (UTC)

I've fixed it. --Zundark (talk) 10:38, 3 February 2008 (UTC)