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

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Advance Math

There exists a group G of order 8 having the followingpresentation: G=?i,j,k | ij=k, jk=I, ki=j, i^2 =j^2 =k^2?. Denotei2bym. 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 thedistinct elements of G. Furthermore, write out the multiplicationtable for G (really, this should be going on while you do the firstpart of the problem).

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