# Math 330/MthT 435

# Abstract Algebra

## Midterm Study Guide

The Midterm exam will be on Friday October 18.

The exam will cover Chapters 1--10. A large
portion of the exam test that you know the important definitions and theorems,
and that you can apply them to study specific examples. For example:
you should know the definition of a cylic group, know the statement of
the Fundamental Theorem of Cylic Groups, and be able to apply it to
find all subgroups of Z_450.

Know all important definitions and how to apply them: groups, subgroups,
cyclic groups,
order of a group, order of an element, Abelian groups, permutation groups,
isomorphism, automorphism, cosets, direct product, normal subgroup,
factor group, homomorphisms, kernels,...

Know how to state and use the important theorems and their corollaries:
Fundamental Theorem of Cylic Groups, Caley's Theorem, Lagrange's Theorem,
Cauchy's Theorem for Abelian Groups, First Isomorphism Theorem for Groups...

Understand the important examples of groups and how to work with
them, such as:
Z, R, R*, C*, Z_n, U(n), D_n, S_n, A_n, GL(n,R), SL(n,R), GL(n,Z_p)...