Sublattices generated by root differences

Let Φ be an irreducible root system of exceptional type. In this paper we calculate the set of exponents of torsion subgroups of quotients ZΦ/L, where ZΦ is the root lattice and L runs through the sublattices thereof which are generated by root differences. The maximum such exponent is of interest b...

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Bibliographic Details
Published in:Journal of algebra 2014-08, Vol.412, p.255-263
Main Author: Lawther, R.
Format: Article
Language:English
Subjects:
Exponents of torsion subgroups
Lifting of embeddings
Root lattices
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Summary:Let Φ be an irreducible root system of exceptional type. In this paper we calculate the set of exponents of torsion subgroups of quotients ZΦ/L, where ZΦ is the root lattice and L runs through the sublattices thereof which are generated by root differences. The maximum such exponent is of interest because it appears in the hypotheses of a result of Liebeck and Seitz concerning lifting of embeddings from finite groups of Lie type to algebraic groups.
ISSN:0021-8693
1090-266X
DOI:10.1016/j.jalgebra.2014.04.018