SOLUTION: Show that the given set with indicated binary operation is a group. And determine if it is Abelian. Z2*Z with operation * defined by (a,s)*(b,t) = (a+bmod2,((-1)^b)s+t)

Algebra ->  Distributive-associative-commutative-properties -> SOLUTION: Show that the given set with indicated binary operation is a group. And determine if it is Abelian. Z2*Z with operation * defined by (a,s)*(b,t) = (a+bmod2,((-1)^b)s+t)      Log On


   

Question 27102: Show that the given set with indicated binary operation is a group. And determine if it is Abelian.
Z2*Z with operation * defined by (a,s)*(b,t) = (a+bmod2,((-1)^b)s+t)
Answer by kev82(151) About Me  (Show Source):
You can put this solution on YOUR website!
Hi,
To show it's a group you must show four things.
1) Closure
2) Associativity
3) Existence of identity
4) Existence of inverses
None of these are particularly difficult, which one are you having trouble with? It doesn't look immediatly associtive, but if you work through it, you will see it is.
To see if the group is abelian you must check if Do the multiplication of two general elements both ways, and see if you get the same thing - you shouldn't.
Write back with the part you are stuck on and I'll see if I can help with that bit specifically.
Hope that helps,
Kev.