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On completely reducible solvable subgroups of GL(n, Δ)

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Abstract

Let Δ be a finite field and denote by GL(n, Δ) the group ofn×n nonsingular matrices defined over Δ. LetR⊆GL(n, Δ) be a solvable, completely reducible subgroup of maximal order. For |Δ|≧2, |Δ|≠3 we give bounds for |R| which improve previous ones. Moreover for |Δ|=3 or |Δ|>13 we determine the structure ofR, in particular we show thatR is unique, up to conjugacy.

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References

  1. J. D. Dixon,The Fitting subgroup of a linear solvable group, J. Aust. Math. Soc.7 (1967), 417–424.

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  2. A. Mann, private communication.

  3. Y. Segev, Ph.D. Thesis, The Hebrew University of Jerusalem, 1984.

  4. D. A. Suprunenko,Matrix Groups, Translations of Mathematical Monographs, Vol. 45, 1976.

  5. T. R. Wolf,Solvable and nilpotent subgroup of GL (n, q m), Can. J. Math.5 (1982), 1097–1111.

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Authors and Affiliations

  1. Institute of Mathematics, The Hebrew University of Jerusalem, Jerusalem, Israel

    Yoav Segev

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  1. Yoav Segev
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This work is part of a Ph.D. thesis done at the Hebrew University under the supervision of Professor A. Mann.

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Segev, Y. On completely reducible solvable subgroups of GL(n, Δ). Israel J. Math. 51, 163–176 (1985). https://doi.org/10.1007/BF02772964

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  • DOI: https://doi.org/10.1007/BF02772964

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