What is the meaning of this expression ?

  • Thread starter zetafunction
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  • #1
[tex] nZ/mZ [/tex]

where / means a quotient group

if n=1 then [tex] Z/mZ [/tex] is the set of integers modulus n {0,1,2,3,4,...,n-1} in case

m=2 we have a binary system, but i do not know what (1) will mean

of ocurse 'Z' means the set of all (positive) integers.
  • #2
What is (1)?

Anyway, this only makes sense if n divides m as you need mZ to be a subgroup of nZ.

In this case you can just factor n out and be left with something isomorphic to Z/m'Z where m=nm'.

They are not equal - the the cosets are different but they are isomorphic.

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