# MATH 322/422 - Modern Algebra

Fall 2015

Professor: Dr. Janet Vassilev
Office: SMLC 324

Office Hours:  M 2 pm, W 11 am-12 noon, F 10 am-11am and by appointment.
Telephone:
(505) 277-2214
email: jvassil@math.unm.edu

webpage: http://www.math.unm.edu/~jvassil

## Cardinality and Equivalence relations

0: 4, 12, 14, 15, 16, 17, 26, 31, 34, 35

1: 32, 34, 36, 37

## Isomorphic Structures

2: 2, 4, 8, 17, 24, 27, 36
3: 2, 4,  16, 27

## Cyclic groups

4: 19, 20(a,b), 25, 29, 32, 35
5:20, 36, 39, 51, 54

## Finitely generated groups

6: 10, 18, 28, 32, 33, 35, 45, 46, 50, 55

## Orbits and cycles

7: 2, 4, 5
8: 2, 4, 6, 8, 32, 35, 36

## Alternating groups

8: 40, 41, 43, 46
9: 2, 9, 12, 16, 23, 29, 31, 34

## Direct products of groups

10: 4, 6, 7 (Use our D_4 with H={e,f_v}), 9, 10 (Use our D_4 with H={e,r^2}), 15, 19, 28, 33, 39, 40

## Homomorphisms

11: 5, 8, 16, 23, 24, 32, 36, 39
13: 4, 5, 33, 34, 49

## Factor Groups

13: 18, 19, 22, 32, 44, 50
14: 3, 10, 15, 23, 27, 31, 34

## Group Actions

14: 33, 35, 36
15: 2, 5, 12, 13, 19, 28, 30, 31, 37

## Group Actions and Counting

16: 1,2, 3, 8, 11, 12, 15
17: 1, 2, 7

## Rings

18: 10, 12, 15, 23, 33, 37, 40, 44, 46, 50, 55

## Fermat's and Euler's Theorems

19: 9, 10, 13, 17, 24, 26, 29
20: 4, 12, 13, 23

## Factorization of polynomials

21:  1, 4, 12
22: 3, 5, 7, 11, 12, 23, 24, 25

## Prime and Maximal Ideals

23: 2, 9, 14, 19, 25, 28, 35
26: 3, 10, 24, 26