Algebra I

22m205, Fall 2007

Instructor: Fred Goodman


I posted solutions to the third assignment, written by Emanoil Theodorescu, see below.

Contact Information:


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



325G Maclean Hall


goodman at math dot uiowa dot edu


Office: 319-335-0791

Paper Mail:

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

Office Hours:

M & W, 12:30 and by appointment




Click this link for the syllabus.


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

This text is required.

Serge Lang (1927-2005)

Additional Recommended texts: 

Nathan Jacobson, Basic Algebra II,  W.H. Freeman, 1989  (seems to be out of print)

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

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

Alperin and Bell, Groups and Representations, Springer Verlag (Graduate Texts in Mathematics No. 162)

Assignment lists:

Details of assignements 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: Due date to be negotiated. From Lang, Chapter1, Exercises 5, 7, 8, 9, 13, 14.

Additional problems: 1) 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).

2) Classifiy non--abelian groups of order 30.

Assignment no 2: click here

Assignment no 3: I have duplicated some pages of exercises from the book of Alperin and Bell. Do the following: From page 26-27, nos. 11-14, from page 80, nos. 7-8, from page 85, nos. 3-4. The last exercises (page 85) are part of a bigger set which are supposed to tell a certain story. We'll finish the story the next time around.

Assignment no 4: click here