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Orientably regular maps with Euler characteristic divisible by few primes

Gill, Nick (2013). Orientably regular maps with Euler characteristic divisible by few primes. Journal of the London Mathematical Society, 88(1) pp. 118–136.

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DOI (Digital Object Identifier) Link: https://doi.org/10.1112/jlms/jdt010
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Abstract

Let G be a (2, m, n)-group and let x be the number of distinct primes dividing χ, the Euler characteristic of G. We prove, first, that, apart from a finite number of known exceptions, a non- abelian simple composition factor T of G is a finite group of Lie type with rank n ≤ x. This result is proved using new results connecting the prime graph of T to the integer x.

We then study the particular cases x = 1 and x = 2. We give a general structure statement for (2, m, n)-groups which have Euler characteristic a prime power, and we construct an infinite family of these objects. We also give a complete classification of those (2, m, n)-groups which are almost simple and for which the Euler characteristic is a prime power (there are four such).

Finally we announce a result pertaining to those (2, m, n)-groups which are almost simple and for which |χ| is a product of two prime powers. All such groups which are not isomorphic to PSL2 (q) or PGL2 (q) are completely classified.

Item Type: Journal Item
Copyright Holders: 2013 London Mathematical Society
ISSN: 1469-7750
Academic Unit/School: Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
Faculty of Science, Technology, Engineering and Mathematics (STEM)
Related URLs:
Item ID: 36570
Depositing User: Nick Gill
Date Deposited: 12 Feb 2013 10:05
Last Modified: 07 Dec 2018 15:05
URI: http://oro.open.ac.uk/id/eprint/36570
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