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This is not a remark on your solutions, but rather a question about the exercises. I hope that’s ok. Pinter, Second edition. Chapter Six, Exercise I. Automata, Semigroups, and Groups....

In Pinter C.2 n is explicitly mentioned as fixed. In C.5 it is "some integer", the selected answers for C.5 prove the case where it is not fixed. The proof...

a * ln(b) is an operation on the set of real numbers, however, the problem, at least in my copy of the book, operates on the set of all real...

1 2 3 4 2 1 4 3 and 1 2 3 4 4 3 2 1 Are also solutions since the negative cancels.

## Chapter 11, Section D, Problem 5 (from the 2nd edition) Let $G$ be a group and let $a,b \in G$. Prove the following: Let ord($a$) = $n$, and suppose...