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Small Groups of Automorphisms
Author(s) -
Pálfy P. P.,
Pyber L.
Publication year - 1998
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609397004037
Subject(s) - mathematics , automorphism , mathematics subject classification , abelian group , nilpotent , automorphisms of the symmetric and alternating groups , pure mathematics , exponent , nilpotent group , class (philosophy) , group (periodic table) , orbit (dynamics) , automorphism group , combinatorics , algebra over a field , linguistics , physics , philosophy , quantum mechanics , artificial intelligence , computer science , engineering , aerospace engineering
Let A be a group of automorphisms of the finite group G such that (∣ A ∣, ∣ G ∣)=1. Then ∣ A ∣<∣ G ∣ 2 , and the exponent 2 here is best possible. If, moreover, A is nilpotent of class at most 2, then ∣ A ∣<∣ G ∣. If A is abelian, then A has a regular orbit on G . 1991 Mathematics Subject Classification 20D45.