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The Fourth Janko Group$
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Alexander A. Ivanov

Print publication date: 2004

Print ISBN-13: 9780198527596

Published to Oxford Scholarship Online: September 2007

DOI: 10.1093/acprof:oso/9780198527596.001.0001

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O 10 + ( 2 ) AS A PROTOTYPE

O 10 + ( 2 ) AS A PROTOTYPE

Chapter:
(p.18) 2 O 10 + ( 2 ) AS A PROTOTYPE
Source:
The Fourth Janko Group
Author(s):

A. A. Ivanov

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198527596.003.0002

This chapter constructs J4 as a completion group which is constrained at level 2 of a certain amalgam G = {G[0],G[1]}. In fact J4 is the only such completion, which proves the uniqueness of J4. The amalgam G is a modification of a classical amalgam H = {H[0],H[1]} contained in the orthogonal group O+ 10(2). The chapter illustrates the strategy by showing that O+ 10 (2) is the only completion group of H which is constrained at level 2. This reproves a special case of a classical result by P. J. Cameron and C. E. Praeger.

Keywords:   dual polar graphs, geometric cubic subgraphs, amalgam H. universal completion

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