On the finite simple images of free products of finite groups | Zendy

King Carlisle S. H. | Zendy

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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.

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