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)

[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 p^n-1 are always normal (see e.g. Frattini subgroup), but not the subgroups of smaller order p^n-j, j ≥ 2.

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