Hi, Algebraists:(adsbygoogle = window.adsbygoogle || []).push({});

The modN reduction map r(N) from a matrix group (any group in which the elements

are matrices over Z-integers) over the integers, in which r is defined by

r(N) : (a_ij)-->(a_ij mod N) is not always commutative, e.g.:

r(6) :Gl(2,Z) --Gl(2,Z/N)

is not onto, since Gl(2,Z) is unimodular over Z, but Gl(2,Z/N) is not, e.g., we can

take units of Z/N that are not 1modN , so that the determinants do not match up;

e.g., for N=10 , take the unit , say, 7 in Z/10Z ; then the matrix M with a_11=7

a_22 =0 and 0 otherwise, is in Gl(2,Z/10) (use, M' with a_11'=3 , and a_22'=1 )

but it is not the image of any matrix in Gl(2,Z), since the determinants do not match

up.

** question **:

Anyone know any results re when the mod2 reduction map r(2) is onto?

Thanks.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Is the Mod2-Reduction Map Onto?

**Physics Forums | Science Articles, Homework Help, Discussion**