Three Substitution Groups. Illustrations of the Symmetric Group S4
In section 8.5 we constructed a field G.F.23 consisting of eight polynomials of degree 2 over the field Z2 using an indeterminate R which satisfied the irreducible cubic equation R3 = R + 1. The seven non-zero elements form a cyclic group under multiplication. This enables us to set out a table of reciprocals among its elements as follows:
KeywordsNormal Subgroup Symmetric Group Substitution Group Ringing Order Element Conjugate
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