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Let m and n be nonzero integers and k and l integers. Show that the .pdf

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Let m and n be nonzero integers and k and l integers. Show that the group has at most mn elements. If k=l=1, show that this group is abelian and has exactly mn elements. How else might you describe that group? Solution The element [n] ? Z/pqZ is a generator if and only if .... (2) The order of ab is equal to the order of ba. ... ?1 ak+1b, as desired.) Since m = o(b?1ab), we have e = (b. ?1 ab)m = b. ?1 ... So, this shows that H ? K is a subset of G which is a group with .... unless l ? k + 1 = 1 or 2, i.e. unless l = k or k + 1.

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Let m and n be nonzero integers and k and l integers. Show that the group has at most mn elements. If k=l=1, show that this group is abelian and has exactly mn elements. How else might you describe that group? Solution The element [n] ? Z/pqZ is a generator if and only if .... (2) The order of ab is equal to the order of ba. ... ?1 ak+1b, as desired.) Since m = o(b?1ab), we have e = (b. ?1 ab)m = b. ?1 ... So, this shows that H ? K is a subset of G which is a group with .... unless l ? k + 1 = 1 or 2, i.e. unless l = k or k + 1

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Let m and n be nonzero integers and k and l integers. Show that the .pdf

  • 1. Let m and n be nonzero integers and k and l integers. Show that the group has at most mn elements. If k=l=1, show that this group is abelian and has exactly mn elements. How else might you describe that group? Solution The element [n] ? Z/pqZ is a generator if and only if .... (2) The order of ab is equal to the order of ba. ... ?1 ak+1b, as desired.) Since m = o(b?1ab), we have e = (b. ?1 ab)m = b. ?1 ... So, this shows that H ? K is a subset of G which is a group with .... unless l ? k + 1 = 1 or 2, i.e. unless l = k or k + 1