There exists a group G of order 8 having the following presentation: G=〈i,j,k | ij=k, jk=I,...

There exists a group G of order 8 having the following presentation: G=〈i,j,k | ij=k, jk=I, ki=j, i^2 =j^2 =k^2〉. Denotei2 bym. Showthat every element of G can be written in the form e, i, j, k, m, mi, mj, mk, and hence that these are precisely the distinct elements of G. Furthermore, write out the multiplication table for G (really, this should be going on while you do the first part of the problem).

Expert Solution

Colby Messinger answered 2 years ago

Consider the group G = {1, −1, i, −i, j, −j, k, −k} under multiplication. Here...

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