On maximal finite irreducible subgroups of . IV. Remarks on even dimensions with applications to

Authors:
Wilhelm Plesken and Michael Pohst

Journal:
Math. Comp. **34** (1980), 259-275

MSC:
Primary 20C10

DOI:
https://doi.org/10.1090/S0025-5718-1980-0551304-9

MathSciNet review:
551304

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Abstract: The general methods for the determination of maximal finite absolutely irreducible subgroups of developed in Part I of this series of papers [6] are refined for even *n*. Applications are made to in view of Part V [7], where a complete classification is obtained.

**[1]**H. BROWN, R. BÜLOW, J. NEUBÜSER, H. WONDRATSCHEK & H. ZASSENHAUS,*Crystallographic Groups of Four-Dimensional Space*, Wiley, New York, 1978.**[2]**E. C. DADE, "The maximal finite groups of integral matrices,"*Illinois J. Math.*, v. 9, 1965, pp. 99-122. MR**0170958 (30:1192)****[3]**I. M. ISAACS,*Character Theory of Finite Groups*, Academic Press, New York, 1976. MR**0460423 (57:417)****[4]**W. PLESKEN, "On absolutely irreducible representations of orders," in*Number Theory and Algebra*(H. Zassenhaus, Editor), Academic Press, New York, 1977. MR**0466192 (57:6072)****[5]**W. PLESKEN, "On reducible and decomposable representations of orders,"*J. Reine Angew. Math.*, v. 297, 1978, pp. 188-210. MR**0466193 (57:6073)****[6]**W. PLESKEN & M. POHST, "On maximal finite irreducible subgroups of . I. The five and seven dimensional cases,"*Math. Comp.*, v. 31, 1977, pp. 536-551. MR**0444789 (56:3137a)****[7]**W. PLESKEN & M. POHST, "On maximal finite irreducible subgroups of . V. The eight dimensional case and a complete description of dimensions less than ten,"*Math. Comp.*, v. 34, 1980, pp. 277-301. MR**551305 (81b:20012c)**

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DOI:
https://doi.org/10.1090/S0025-5718-1980-0551304-9

Keywords:
Integral matrix groups

Article copyright:
© Copyright 1980
American Mathematical Society