Irreducible Finite Integral Matrix Groups of Degree 8 and 10 Bernd
نویسنده
چکیده
The lattices of eightand ten-dimensional Euclidean space with irreducible automorphism group or, equivalently, the conjugacy classes of these groups in GL„(Z) for n = 8, 10, are classified in this paper. The number of types is 52 in the case n = 8 , and 47 in the case n = 10. As a consequence of this classification one has 26, resp. 46, conjugacy classes of maximal finite irreducible subgroups of GL8(Z), resp. GLio(Z) . In particular, each such group is absolutely irreducible, and therefore each of the maximal finite groups of degree 8 turns up in earlier lists of classifications.
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