# Content of the book “Group Theory Seminar Lectures:1960-1961”

Is there any one who read the book "Group Theory Seminar Lectures:1960-1961"? Please tell me the content about this book.

We know in 60s, there are many important results. N. Blackburn is one of my favorite group theorists. I want to know the content of this book. But there is no information I can find.

• I suspect -and this is only a guess, because I cannot find anything about this book anywhere- that this book covers the group theory seminars from 1960-1961 at the University of Manchester (if my memory serves me correctly, Blackburn was at Manchester during this period). Manchester at this time was an exciting place for group theory - this was the golden age of group theory, and Manchester was the focal point. Indeed, combinatorial group theory came of age as a subject in Manchester during this period, with the help of B.H. Neumann and those around him. – user1729 Jan 13 '14 at 11:57
• For example, in the 50s Gilbert Baumslag had completed his PhD under Neumann, and Higman was a lecturer. Note also that Hanna Neumann was there also (B.H.'s wife, and a formidable group-theorist in her own right). An impressive cast! – user1729 Jan 13 '14 at 11:59
• As I know, Blackburn focus on finite groups, epically on finite p-groups. I remember in 1960-1961, there was a seminar in Chicago on group theory. – Wei Zhou Jan 14 '14 at 0:54
• I hope someone who read this book will give us more information about this book. – Wei Zhou Jan 14 '14 at 14:01
• Here are some library records: worldcat.org/oclc/20184380 worldcat.org/oclc/8212406 worldcat.org/oclc/258342739 One indicates the lectures were at Chicago. – Jack Schmidt Jan 16 '14 at 2:03

## 1 Answer

Preface: This document is being issued at the end of a Special year program on the theory of groups at the University of Chicago from October 1, 1960 to June 30, 1961. It contains summaries of papers presented at the weekly seminar which was one of the principal features of the program.

Since John Thompson does not plan to submit his paper on Groups of odd order $$p^aq^b$$ for publication in the near future it is presented here in greater detail than the other papers. The great majority of the summaries are of results to appear within a year.

The mathematical community is grateful to the National Science Foundation, the OPffice of Scientific Research of the Air Force, and the Esso Foundation for their support of the program.

-- James Boen, July 1, 1961.

Table of contents:

• N Blackburn, $$p$$-groups of maximal class (5 pages)
• G Higman, Enumerating $$p$$-groups (7 pages)
• W Feit– JG Thomspon, Groups with a faithful rep of degree $$\leq \frac{p-1}{2}$$ (2 pages)
• M Suzuki, On finite CN groups of even order and related groups (3 pages)
• JG Thompson, On groups of odd order $$p^a q^b$$ (20 pages)
• JA Green, Representations and Characters (9 pages)
• J Alperin, Automorphisms of Solvable Groups (3 pages)
• DG Higman, Flag-transitive groups (3 pages)
• N Ito, On a class of doubly transitive groups (2 pages)
• D Gorenstein–J Walker, On finite groups with dihedral sylow 2-subgroups (7 pages)
• D Tamari, Monoids and word problem for groups (1 page)
• N Jacobson, Cayley Planes (1 page)
• N Blackburn, Cernikov $$p$$-groups (1 page)
• E Parker, Orthogonal latin squares of order 10 (2 pages)
• H Wielandt, Transfer theorems (4 pages)
• G Higman, Suzuki 2-groups (1 page)
• R Brauer, Groups of even order (4 pages)
• J Britton, The word problem (5 pages)
• P Fong, Modular representations of solvable groups (1 page)
• OH Kegel, On subnormal subgroups of finite groups (5 pages)
• H Wielandt, General theory of permutation groups (6 pages)
• M Suzuki, Groups with a partition (1 page)
• I haven't had a chance to read any yet, but expect to do so next weekend. – Jack Schmidt Jan 20 '14 at 23:09
• It seems that most are just the abstract of the topics by the length. I'm interested in the paper of Thomson, – Wei Zhou Jan 20 '14 at 23:33
• Thompson: The result is the same as Goldschmidt (1970) ams.org/mathscinet-getitem?mr=276338 but the proof is much, much longer and I think harder. It appears to use lots of ideas from Thompson's later work (I guess the Thompson subgroup was 1964, there are lots of normalizers of higher rank el ab subgroups in this). – Jack Schmidt Jan 21 '14 at 2:56
• Thanks! By the way, is there anyone give some lecture notes helping the student of Ph. D. level to understand the origional proof of odd order theorem by Feit and Thompson? I know Bender and Glaumberman had published a book about this theorem. But I find more interesting in the origional proof. – Wei Zhou Jan 21 '14 at 13:38
• I don't know of any such notes. I found Gorenstein's finite groups to be a decent lead in to the CA/CN papers of Suzuki et al. which then lead to Feit-Thompson. However, I think Bender and Glauberman's work greatly simplifies things: compare Thompson's 1960 to Goldschmidt's 1970 and notice the key new ingredients come from (Goldschmidt,) Bender and Glauberman. – Jack Schmidt Jan 21 '14 at 16:28