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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Under the degree of some finite linear groups. II


Author: Harvey I. Blau
Journal: Trans. Amer. Math. Soc. 203 (1975), 87-96
MSC: Primary 20C20
DOI: https://doi.org/10.1090/S0002-9947-1975-0379651-9
MathSciNet review: 0379651
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Abstract: Let $ G$ be a finite group with a cyclic Sylow $ p$-subgroup for some prime $ p \geq 13$. Assume that $ G$ is not of type $ {L_2}(p)$, and that $ G$ has a faithful indecomposable modular representation of degree $ d \leq p$. Some known lower bounds for $ d$ are improved, in case the center of the group is trivial, as a consequence of results on the degrees $ \pmod p$ of irreducible Brauer characters in the principal $ p$-block.


References [Enhancements On Off] (What's this?)

  • [1] H. I. Blau, Under the degree of some finite linear groups, Trans. Amer. Math. Soc. 155 (1971), 95-113; Errata, ibid. 162 (1971), 475. MR 43 #367; 44 #329. MR 0274604 (43:367)
  • [2] -, Finite groups where two small degrees are not too small, J. Algebra 28 (1974), 551-555. MR 0437629 (55:10553)
  • [3] W. Feit, Groups with a cyclic Sylow subgroup, Nagoya Math. J. 27 (1966), 571-584. MR 33 #7404. MR 0199255 (33:7404)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1975-0379651-9
Keywords: Indecomposable modular representation, small degree, cyclic Sylow $ p$-subgroup, main value
Article copyright: © Copyright 1975 American Mathematical Society

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