Definitely index 2: H = L union (L + (1/2, 1/2, 1/2, 1/2)) You might be getting confused with the fact that the Lipschitz quaternions of unit norm (abstractly Q_8) form an index-3 normal subgroup of the Hurwitz quaternions of unit norm (abstractly 2T): http://en.wikipedia.org/wiki/Binary_tetrahedral_group This is in turn an index-5 abnormal subgroup of the icosians of unit norm (abstractly 2I): http://en.wikipedia.org/wiki/Icosian APG
Sent: Tuesday, March 10, 2015 at 3:38 PM From: "Fred Lunnon" <fred.lunnon@gmail.com> To: math-fun <math-fun@mailman.xmission.com> Subject: [math-fun] Hurwitz integers --- and it sez 'ere ...
https://en.wikipedia.org/wiki/Hurwitz_quaternion
<< The Lipschitz quaternions L form an index 2 sublattice of H. >>
"index 3" , I think ?! See eg. Conway & Smith sect. 5.5 .
WFL
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