Sporadic simple group
From Encyclopedia of Mathematics
A simple finite group that does not belong to any of the known infinite series of simple finite groups. The twentysix sporadic simple groups are listed in the following table.'
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References
[1]  S.A. Syskin, "Abstract properties of the simple sporadic groups" Russian Math. Surveys , 35 : 5 (1980) pp. 209–246 Uspekhi Mat. Nauk , 35 : 5 (1980) pp. 181–212 
[2]  M. Aschbacher, "The finite simple groups and their classification" , Yale Univ. Press (1980) 
Comments
The recent classification of the finite simple groups (1981) has led to the conclusion that — up to a uniqueness proof for the Monster as the only simple group of its order with certain additional properties — every nonAbelian finite simple group is isomorphic to: an alternating group on at least letters, a group of (twisted or untwisted) Lie type, or one of the above sporadic groups. See [a2] for a discussion of the proof.
References
[a1]  J.H. Conway, R.T. Curtis, S.P. Norton, R.A. Parker, R.A. Wilson, "Atlas of finite groups" , Clarendon Press (1985) 
[a2]  D. Gorenstein, "Finite simple groups. An introduction to their classification" , Plenum (1982) 
How to Cite This Entry:
Sporadic simple group. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Sporadic_simple_group&oldid=11475
Sporadic simple group. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Sporadic_simple_group&oldid=11475
This article was adapted from an original article by V.D. Mazurov (originator), which appeared in Encyclopedia of Mathematics  ISBN 1402006098. See original article