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Quasiprimitive Groups with No Fixed Point Free Elements of Prime Order
Author(s) -
Giudici Michael
Publication year - 2003
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610702003812
Subject(s) - mathematics , conjugacy class , combinatorics , prime (order theory) , fixed point , permutation group , wreath product , order (exchange) , classification of finite simple groups , group (periodic table) , p group , conjecture , primitive permutation group , transitive relation , simple group , permutation (music) , simple (philosophy) , product (mathematics) , symmetric group , pure mathematics , group theory , group of lie type , cyclic permutation , geometry , philosophy , mathematical analysis , chemistry , acoustics , epistemology , physics , organic chemistry , finance , economics
The paper determines all permutation groups with a transitive minimal normal subgroup that have no fixed point free elements of prime order. All such groups are primitive and are wreath products in a product action involving M 11 in its action on 12 points. These groups are not 2‐closed and so substantial progress is made towards asserting the truth of the polycirculant conjecture that every 2‐closed transitive permutation group has a fixed point free element of prime order. All finite simple groups T with a proper subgroup meeting every Aut( T )‐conjugacy class of elements of T of prime order are also determined.