Mark each of the following true or false.—a. If G1 and G2 are any groups, then G1 X G2 is...

Mark each of the following true or false.

—a. If G1 and G2 are any groups, then G1 X G2 is always isomorphic to G2 X G1.

— b. Computation in an external direct product of groups is easy if you know how to compute in each component group.

—c. Groups of finite order must be used to form an external direct product.

—d. A group of prime order could not be the internal direct product of two proper nontrivial subgroups.

— e. ℤ2 X ℤ4 is isomorphic to ℤ8.

— f. ℤ2 X ℤ4 is isomorphic to S8.

— g. ℤ3 X ℤ8 is isomoiphic to S4.

— h. Every element in ℤ4 X ℤ8 has order 8.

— i. The order of ℤ2 X ℤ15 is 60.

— j. ℤ,„ X ℤ„ has mil elements whether in and n are relatively prime or not.