CH 5 - Direct Products and Finite Abelian Groups

Question 1

Define the direct product of two groups.

State a theorem on G x H and its order.

Answer 1

Question 2

Define G-bar and H-bar and state a theorem on their 4 properties within GxH.

State a theorem on two quotient groups isomorphic to G and H.

Answer 2

Question 3

When is a group G directly (in)decomposable?

State a theorem on normal subgroups and direct products.

Answer 3

Question 4

Define the direct product of multiple groups.

State four properties of the direct product of multiple groups.

State a theorem on normal subgroups and direct products of multiple groups.

State a theorem to find normal subgroups of direct products (using quotients).

Answer 4

Question 5

State a lemma and a corollary on the direct product of cyclic groups.

State the Fundamental Theorem of Finite Abelian Group.

State the Fundamental Theorem of Finite Abelian Groups, Version II.

Answer 5