Math 360, Fall 2017, Assignment 5

I tell them that if they will occupy themselves with the study of mathematics, they will find in it the best remedy against the lusts of the flesh.

- Thomas Mann, The Magic Mountain

Carefully define the following terms, then give one example and one non-example of each:

1. Group of units (of a monoid).
2. Subgroup.
3. Subgroup generated by a subset.

Carefully state the following theorems (you do not need to prove them):

1. Theorem concerning intersections and unions of subgroups.

Solve the following problems:

1. Section 5, problems 1, 2, 3, 4, 5, 6, 7, 8, 11, 12, 22, and 23.

--------------------End of assignment--------------------