Homework Assignment for Math 830 (Algebra), Line # 17014, Fall 2006.

Homework Assignment - I

• Due date: Friday, September 15th.

• From "Progress Check - II", problems [II], [V], [VI].

• From "Progress Check - III", problem [II], and also the following:

• If f : G_1 -> G_2 is an isomorphism, then

f^{-1} : G_2 -> G_1 is an isomorphism.

• If f : G_1 -> G_2 and g : G_2 -> G_3 are isomorphisms, then

g f : G_1 -> G_3 (the composition) is an isomorphism.

• If f : G_1 -> G_2 is an isomorphism, then

f (1) = 1, and f(x)^{-1} = f(x)^{-1} hold (x in G_1).

• If f : G_1 -> G_2 is an isomorphism, then

ord (f (x)) = ord x holds for x in G_1.

• Find an example of a group G such that ord G = infinity,

and such that ord x is finite, for an arbitrary x in G.

Last Updated: 6:43PM, 09/17/06