Math 308 Exam 2 Review
The second midterm will be held in class on Monday, April 6. It
will be a closed-book, closed-notes exam, and will cover all class
material from sections 10-16 and 18-21 of the textbook. Earlier
material will not be explicitly tested, but of course it may be
necessary background.
You will be asked for complete definitions (including appropriate context,
e.g., the index of what?) of some subset of
the following terms:
- coset (be able to distinguish between left and right cosets)
- index
- direct product of groups
- group of symmetries
- (group) homomorphism
- kernel
- normal
- factor group / quotient group
- conjugate
- conjugation
- automorphism
- inner automorphism
- simple
- center
- commutator subgroup
- action
- transitive action
- isotropy subgroup
- orbit (in the context of group actions)
- ring
- (ring) homomorphism
- (ring) isomorphism
- commutative ring
- ring with unity
- unit
- division ring
- field
- zero divisor
- cancellation laws
- integral domain
- characteristic
- Euler totient function (or phi-function)
- field of quotients
Believe it or not, this is fewer terms than for the last exam.
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