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Infinite Simple (2, 3, n )‐Groups and Congruence Hulls in the Modular Group
Author(s) -
Mason A. W.,
Pride S. J.
Publication year - 1999
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/s002460939900586x
Subject(s) - mathematics , congruence (geometry) , simple group , simple (philosophy) , modular group , combinatorics , group (periodic table) , modular design , modular form , mathematics subject classification , pure mathematics , geometry , philosophy , chemistry , organic chemistry , epistemology , computer science , operating system
We prove that if n > 66 and ( n , 30) = 1, then there exist uncountably many infinite simple (2, 3, n )‐ groups, that is, groups generated by a pair of elements x , y , say, where the orders of x , y and xy are 2, 3 and n , respectively. This extends previous results of Schupp and the authors. These results are used to prove the existence of subgroups of the modular group with special arithmetic properties. 1991 Mathematics Subject Classification 20F06.