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On the finite simple images of free products of finite groups
Author(s) -
King Carlisle S. H.
Publication year - 2019
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/plms.12184
Subject(s) - mathematics , simple (philosophy) , classification of finite simple groups , simple group , conjecture , rank (graph theory) , order (exchange) , group of lie type , finite group , combinatorics , free product , group (periodic table) , image (mathematics) , ca group , pure mathematics , product (mathematics) , group theory , geometry , abelian group , computer science , artificial intelligence , philosophy , chemistry , organic chemistry , epistemology , finance , economics
Given non‐trivial finite groups A and B , not both of order 2, we prove that every finite simple group of sufficiently large rank is an image of the free product A * B . To show this, we prove that every finite simple group of sufficiently large rank is generated by a pair of subgroups isomorphic to A and B . This proves a conjecture of Tamburini and Wilson.