Which topics and theorems do you think are the most important out of those we have studied?
None. Just figure out the definitions and true-false statements, and examples...that is the only place I lose points, not on understanding or applying relevant information...
What kinds of questions do you expect to see on the exam?
Provide an example of a group...
What do you need to work on understanding better before the exam?
Examples of all the different possible kinds of groups that we could be asked to show examples of on the test...
Come up with a mathematical question you would like to see answered or a problem you would like to see worked out in class on Wednesday.
Examples.
Abelian
Non Abelian
Quotient Group
Non trivial subgroup
Group isomorphism for Z4 and Z2 x Z2
Kernal
Non-abelian groups: Sn, An, Dn, matrix groups.
Abelian groups: Z, Zn, Un.
An element of finite order contained in a group of infinite order.
Cyclic groups of all orders—both infinite and finite.
Groups which are not cyclic, including a (sub)group generated by two elements which is not cyclic.
A group with a non-trivial center.
A subgroup of an infinite group that has finite index
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