Odd Characterisations of Finite Simple Groups

Автор(ы):Graham Higman
Год изд.:1968
Описание: The purpose of these notes is to illustrate some techniques in modern finite group theory by describing their application in particular cases. These applications are to characterisations of simple groups which, for the most part, are odd in two senses of the word: They are characterisations of individual groups rather than whole classes, and they are characterisations in terms of properties of subgroups of odd order. I believe them to be rather suitable for beginners to cut their teeth on, because they are neither so trivial that the principles are not illustrated nor so complicated that the fog of detail obscures everything. However, the choice does mean that a number of topics important for the theory of finite simple groups are omitted (for instance, modular characters).
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Introduction [1]
1. From group theory to characters [1]
2. From characters to group theory [6]
3. An even characterization [9]
4. Self centralisation system on type (3(a)), a even [13]
5. Self centralisation of type (2) [16]
6. Self centralisation of type (2, 2) [18]
7. Some non existence theorems [22]
8. A digression on actions of PSl on 2-groups [23]
9. Self centralizing cyclic subgroups of order 3 [31]
10. Self centralisation system of type (2). The present state of knowledge [43]
11. A characters of PSU [46]
12. Janko’s group of order 175,650 [58]
13. COO-groups [67]
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