Glasnik Matematicki, Vol. 58, No. 2 (2023), 289-305. \( \)

THE NON-EXISTENCE OF A SUPER-JANKO GROUP

Alexander A. Ivanov

Institute for System Analysis ERC, CSC RAS, Moscow, Russia
e-mail:babymonster4371@hotmail.com

Abstract.   Locally projective graphs in Mathieu–Conway–Monster series appear in thin–thick pairs. A possible thick extension of a thin locally projective graph associated with the fourth Janko group has been questioned for a while. Such an extension could lead, if not to a new sporadic simple group, to something equally exciting. This paper resolves this issue ultimately in the non-existence form confirming that the list of 26 sporadic simple groups, although mysterious, is now stable. The result in fact concludes the classification project of locally projective graphs, which has been running for some twenty years.

2020 Mathematics Subject Classification.   20D05, 20D06, 20D08

Key words and phrases.   Locally projective graphs, sporadic groups, geometries

Full text (PDF) (access from subscribing institutions only)

https://doi.org/10.3336/gm.58.2.09

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