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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

# TOWARDS 2 + 1 + 12 ·   3 ·   Aut   ( M 22 )

Chapter:
(p. 76 ) 5 TOWARDS $2 + 1 + 12 · 3 · Aut ( M 22 )$
Source:
The Fourth Janko Group
Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198527596.003.0005

This chapter shows that N[3] is the extraspecial group Q[3] ≅ 21+12 + extended by a group R of order 3 acting fixed-point freely on Q[3]/Z[3] (where Z[3] is the centre of Q[3]/) and that G[3] is the automorphism group Aut (M22) of the sporadic Mathieu group M22. Shpectorov's geometric characterization of M22 in terms of a Petersen type geometry is used. The sporadic Mathieu group M22 appears before any specific completions of G can be considered.

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