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Alternating Groups Acting on Finite Linear Spaces
Author(s) -
Camina Alan R.,
Neumann Peter M.,
Praeger Cheryl E.
Publication year - 2003
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/s0024611503014060
Subject(s) - mathematics , transitive relation , automorphism , simple group , simple (philosophy) , covering groups of the alternating and symmetric groups , classification of finite simple groups , space (punctuation) , line (geometry) , group (periodic table) , mathematics subject classification , pure mathematics , alternating group , automorphisms of the symmetric and alternating groups , group of lie type , combinatorics , group theory , cyclic group , geometry , non abelian group , computer science , philosophy , abelian group , chemistry , organic chemistry , epistemology , operating system
This is a contribution to the study of line‐transitive groups of automorphisms of finite linear spaces. Groups which are almost simple are of particular importance. In this paper almost simple line‐transitive groups whose socle is an alternating group are classified. It is proved that the only alternating groups to occur are those of degrees 7 and 8, and that only one linear space occurs, namely a well‐known space with 15 points and 35 lines. Although much of the proof exploits special properties of alternating groups, some general theory of groups acting line‐transitively on finite linear spaces is developed. 2000 Mathematics Subject Classification 05B05, 20B25.