In Exercises and correct the definition of the italicized term without reference to the te...

In Exercises and correct the definition of the italicized term without reference to the text, if correction is needed, so that it is in a form acceptable for publication. Mark each of the following true or false.

__ a. Every subgroup of every group has left cosets.

__ b. The number of left cosets of a subgroup of a finite group divides the order of the group.

__ c. Every group of prime order is abelian.

__ d. One cannot have left cosets of a finite subgroup of an infinite group.

__ e. A subgroup of a group is a left coset of itself.

__ f. Only subgroups of finite groups can have left cosets.

__ g. An is of index 2 in Sn for n > 1.

__ h. The theorem of Lagrange is a nice result.

__ i. Every finite group contains an element of every order that divides the order of the group.

__ j. Every finite cyclic group contains an element of every order that divides the order of the group.