CMPE 220
HW #6
DUE: 3.1.2003 Friday at
1. Let G be the
group of integers under the operation of addition, and G’ be the group of all
even integers under the operation of addition. Show that the function f: G à G’ defined
by f(a)=2a is an isomorphism.
2. Determine if
the following structure [S,.] is semigroup,
monoid, group or none of these. Name the identity
element if the structure is group or monoid.
·
S = N x N; (x1,y1) . (x2,y2)
= (x1+x2, y1y2)
3. Determine
whether the given function is homomorphism from the group on the left to the
one on the right. Is it also isomorphism?
·
[R*, . ] , [R*, . ] (where R*
denotes the set of nonzero real numbers); f(x)
= |x|