Structure and Representations of Q-groups
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1084 Dennis Kletzing
Structure and Representations of Q-Groups
Springer-Verlag Berlin Heidelberg New York Tokyo 1984
Author
Dennis Kletzing Department of Mathematics and Computer Science Stetson University DeLand, Florida 32720, USA
AMS Subject Classification (1980): 20C, 20 E, 13H ISBN 3-540-13865-X Springer-Verlag Berlin Heidelberg New York Tokyo ISBN 0-387-13865-X Springer-Verlag New York Heidelberg Berlin Tokyo
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© by Springer-Verlag Berlin Heidelberg 1984 Printed in Germany Printing and binding: Beltz Offsetdruck, Hemsbach / Bergstr. 2146/3140-543210
Preface
These notes span a decade of research and reflect the contributions of many individuals. There is one person, however, who has influenced this work to the extent that it would not exist were it not for his constant support and encouragement. He is Professor Ernst Snapper of Da.rtrrDuth College. It is with sincere express my appreciation to him for many, many years of mathematical
that I and
unselfish friendship. I also wish to thank Dr. John Rasmussen for many stimulating conversations. Finally, this work was supported by research grants received from Stetson Uni versi ty. It was writ.ten while on sabbatical leave at Da.rtrrDuth
DeLand, Florida July, 1984
Dennis Kletzing
Introduction Notation .
5
1:..
7
Chapter 1.
Basic
2.
Structure of Q-groups having abelian or dihedral Sylow 2-subgroups
of Q-groups
8
and involutory Q-groups
3.
20 24
4.
Solvable Q-groups . . . .
39
5.
The partially ordered set defined by a Q-group
47
Constructions
58
Q-Groups
1.
Wreath products .
59
2.
Semi-direct products
77
3.
App.L:1Ccl.tl_on to the Weyl groups of types
4.
Theory of transversal pernartat ion r-epr-aserrrat.i.ons
Chapter 3.
and D
n
93 97
105
Local
1.
Closed algebras. The local
no
2.
Local idempotents
130
3•
The combinatorics of p-classes
4•
Local restriction and local induction
5•
The local subgroup
6.
Local multiplicities
Chapter
The local induction prin(:iI)le
143 159 161 174
Representations
1.
The local invariants
180
2.
The local character ring rCGV)V
187
3.
Local splitting
207
.
VI
Application to the Weyl Groups of Exceptional
220 221
1.
F
2.
E S
233
3.
E
240
4.
E
4
7
243
8
Appendix . .
2S9
The character table of F4
270
rl*(F
271
.
4)
The character table of F4/Center
272
rl*(F
273
4/Center)
. .
Conjugacy classes of E S
274
The character table of E S
275
rl*CE
27S
.
S)
•.. . .
+
277
ConJugacy classes of E 7
+
The character table of E 7
278
"r\;'(E+) 7
280
•••••
Conjugacy classes of E
8
281
References
283
Ind
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