Abstract
For each of fifteen of the sporadic finite simple groups we determine the suborbits of its automorphism group in its conjugation action upon its involutions. Representatives are obtained as words in standard generators.
Highlights
For a finite group with at least two conjugacy classes of involutions the Thompson order formula ([11], Theorem 35.1) gives its order using data closely associated with the involutions
This paper studies the involutions in Aut(K) where K is a small sporadic finite simple group
Further suppose that we have identified the subgroup L = ⟨x, y⟩ as being isomorphic to G via recognizing x and y as standard generators. (See [21] for a discussion of standard generators.) we may translate our information from G to L so that we see how L acts upon its involution conjugacy classes within the group H
Summary
Sometimes they have cameo roles; other times they are centre stage. Involutions can often have a considerable influence on the structure of the group to which they belong Even their absence can be telling— witness the Feit Thompson theorem [9]. For a finite group of even order, Brauer and Fowler [10] establish many results concerning involutions and other properties of the group. For a finite group with at least two conjugacy classes of involutions the Thompson order formula ([11], Theorem 35.1) gives its order using data closely associated with the involutions. This paper studies the involutions in Aut(K) where K is a small sporadic finite simple group. It goes without saying that we use the Atlas notation and conventions as given in [20]
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