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.
HVAC System | Audit of HVAC System | Audit and regulatory Comploance.pptx
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
![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](https://image.slidesharecdn.com/letmandnbenonzerointegersandkandlintegers-230324015903-ac912329/85/Let-m-and-n-be-nonzero-integers-and-k-and-l-integers-Show-that-the-pdf-1-320.jpg)
