Three Substitution Groups. Illustrations of the Symmetric Group S4

  • Joan M. Holland
Part of the Introductory Monographs in Mathematics book series (INMOMA)


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:


Normal Subgroup Symmetric Group Substitution Group Ringing Order Element Conjugate 
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Copyright information

© Joan M. Holland 1972

Authors and Affiliations

  • Joan M. Holland
    • 1
  1. 1.Bishop Otter CollegeChichesterUK

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