Professor Chris Parker

Professor Chris Parker

School of Mathematics
Professor of Pure Mathematics

Contact details

+44 (0) 121 414 6199
+44 (0) 121 414 3389
School of Mathematics
Watson Building
University of Birmingham
B15 2TT

School web page:


  • BSc (Birmingham)
  • MSc (Manchester)
  • PhD (Mathematics, Manchester 1988)



My main research interests are in group theory.

Recently my research has been focussed on theorems designed to recognise simple groups from some fragment of their p-local subgroup structure. These theorems are intended to be used in the projects aimed at understanding the classification of the finite simple group. For example together with Stroth(Halle) and Rowley(Manchester), I have shown that many of the finite simple group can be identified from the structure of the centralizer of an element of order $3$.

I am also interested in research which applies the classification of finite simple group. In work with Kay Magaard (Birmingham) and Ben Fairbairn (Birkbeck) I have determined those quasisimple groups which can be used to construct a Beauville surface. I have also studied the commuting graph of a finite group and with my student Luke Morgan have shown that the diameter of a connected component of such a graph has diameter at most 10.


A full listing can be found at



 'On a class of affine geometries' with Sergey Shpectorov and Corneliu Hoffman, Advances in Geometry . Advances in Geometry. 12 (2012), Pages 381–399, 

'A note on groups in which the centraliser of every element of order 5 is a 5-group' with Sarah Astill and  Rebecca Waldecker, Siberian mathematical journal 53 (2012), 781--791

'Completely reducible subcomplexes of spherical buildings' with Katrin Tent, Arch. Math. (Basel) 97 (2011), no. 2, 125--128.

'Strongly p-embedded subgroups' with Gernot Stroth, Pure Appl. Math. Q.  7  (2011),  no. 3, Special Issue: In honor of Jacques Tits, 797--858.

'Recognising simplicity of black-box groups by constructing involutions and their centralisers' with Robert Wilson, J. Algebra 324 (2010), no. 5, 885–915.

'A 3-local characterization of Co_2', with Peter Rowley, J. Algebra 323 (2010), no. 3, 601--621.

'Two families of exotic fusion systems' with Murray Clelland, J. Algebra 323 (2010), no. 2, 287–304.

'Strongly $p$-embedded subgroups of Lie Rank 2', with Gernot Stroth, Arch. Math. (Basel) 93 (2009), no. 5, 405--413.

'A 3-local characterization of M_12 and SL_3(3)', with Sarah Astill, Arch. Math. (Basel) 92 (2009), no. 2, 99--110.