Consider the set G = {1, i, j, k} with multiplication given by i 2 = j
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Consider the set G = {±1, ±i, ±j, ±k} with multiplication given by i2 = j2 = k2 = -1; ij = k; jk = i, ki =j; ji = -k, kj = -i, ik = -j, and the usual rules for multiplying by ± 1. Show that G is a group isomorphic to the quaternion group Q8.
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To show that G is a group isomorphic to the quaternion group Q8 we need to show that G satisfies the ...View the full answer
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Related Book For
Algebra Graduate Texts In Mathematics 73
ISBN: 9780387905181
8th Edition
Authors: Thomas W. Hungerford
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