Abstract Algebra: Theory and Applications · Problem Sage-1

Permutation Groups — Thomas Judson

Mathematics — Abstract Algebra · cyclic-groups-units-sage

Problem

Execute the statement R = Integers(40) to create the set [0,1,2,…,39][0,1,2,\ldots,39]. This is a group under addition mod 40, which we will ignore. Instead we are interested in the subset of elements which have an inverse under multiplication mod 40. Determine how big this subgroup is by executing the command R.unit\_group\_order(), and then obtain a list of these elements with R.list\_of\_elements\_of\_multiplicative\_group().

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