# Contact Information:

### Lectures:

11:30A - 12:20P MWF 118 MLH

### Office:

325G Maclean Hall

### Email:

goodman at math dot uiowa dot edu

### Phone:

Office: 319-335-0791

### Paper Mail:

Fred Goodman
Department of Mathematics MLH
The University of Iowa
Iowa City, IA 52242-1419 USA

tba

# Syllabus:

Click this link for the syllabus.

# Textbooks:

Alperin & Bell, Groups and Representations, Springer Verlag (Graduate Texts in Mathematics No. 162) . This text is required.

Donald Passman, A Course in Ring Theory (AMS Chelsea Publishing). Recommended. I haven't yet figured out how required it will be.

Nathan Jacobson, Basic Algebra II,  W.H. Freeman, 1989  (out of print; I will make some chapters accessible to you).

David Dummit and Richard Foote,  Abstract Algebra,  3rd edition, John Wiley 2003.

Thomas W. Hungerford,  Algebra,  Springer Verlag (Graduate Texts in Mathematics No. 73).

Martin Isaacs, Finite Group Theory, AMS (Graduate Studies in Mathematics) 2008.

Serge Lang, Algebra, Springer Verlag (Graduate Texts in Mathematics No. 211).

# Assignment lists:

Details of assignments will appear here as the assignments are made. Please see the remarks on the syllabus about the standard of explanation expected on the homework.

Assignment no. 1: Exercises 1-8 on pages 35-36 of Alperin & Bell.

Assignment no. 2: Exercises 1-5 and 7-8 on pages 70-71 of Alperin & Bell. Also:

(A) Classify all non-abelian groups of size equal to 30. It is helpful to look at Goodman, Algebra Abstract and Concrete, Example 5.4.14 and exercises 5.4.6 an 5.4.7.

(B) Show that the groups of signed n--by--n matrices is isomorphic to the wreath product of Z_2 with S_n, that is the semi--direct product of

Z_2 \times Z_2 \times ... \times Z_2

(n--fold direct product) with the permutation group S_n.

(C) Find out if every automorphism of a quotient A/K of a finite cyclic group A lifts to an automorphism of A. Use the to find out if two homomorphisms of a finite cyclic group G into the automorphism group of another group N yield isomorphic semidirect products, assuming that the homomorphisms have the same range in Aut(N).

Assignment no. 3: Exercises 1-7, pages 47-48 of Alperin & Bell. (If you manage to do #5, you are required to transfer to the U. of Chicago and study with Alperin.)

Assignment no. 4: Exercises 8-9 pages 47-48; Exercises 2, 3 6 page 61; Exercises 3, 4 page 104. (All page numbers are from Alperin & Bell.)