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Communications in Algebra Volume 45, 2017 - Issue 12
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Original Articles

On the torsion units of the integral group ring of finite projective special linear groups

Ángel del RíoDepartment of Mathematics, University of Murcia, Murcia, SpainCorrespondence[email protected]
&
Mariano SerranoDepartment of Mathematics, University of Murcia, Murcia, Spain
Pages 5073-5087 | Received 04 Jan 2017, Published online: 04 May 2017

References

  • Alperin, J. L. (1986). Local Representation Theory, volume 11 of Cambridge Studies in Advanced Mathematics. Cambridge University Press. Modular representations as an introduction to the local representation theory of finite groups.
  • Berman, S. D. (1955). On the equation xm = 1 in an integral group ring. Ukrain. Mat. Ž. 7:253–261.
  • Bächle, A., Margolis, L. (2016). On the prime graph question for integral group rings of 4-primary groups ii. https://arxiv.org/abs/1606.01506.
  • Bächle, A., Margolis, L. (2014). Rational conjugacy of torsion units in integral group rings of non-solvable groups. Proceedings of the Edinburgh Math Society, published March, 2017: https://doi.org/10.1017/S0013091516000535.
  • Bächle, A., Margolis, L. (2015.) Help – a gap-package for torsion units in integral group rings. http://arxiv.org/abs/1507.08174.
  • Brauer, R., Nesbitt, C. (1941). On the modular characters of groups. Ann. of Math. (2) 42:556–590.
  • Burkhardt, R. (1976). The decomposition matrices of the groups PSL(2,pf). J. Algebra 40(1):75–96.
  • Caicedo, M., Margolis, L., del Río, Á. (2013). Zassenhaus conjecture for cyclic-by-abelian groups. J. Lond. Math. Soc. (2) 88(1):65–78.
  • Gildea, J. (2013). Zassenhaus conjecture for integral group ring of simple linear groups. J. Algebra Appl. 12(6):1350016.
  • Hertweck, M. (2006). On the torsion units of some integral group rings. Algebra Colloq. 13(2):329–348.
  • Hertweck, M. (2007). Partial augmentations and Brauer character values of torsion units in group rings. https://arxiv.org/abs/math/0612429v2
  • Hertweck, M. (2008). Zassenhaus conjecture for A6. Proc. Indian Acad. Sci. Math. Sci. 118(2):189–195.
  • Higman, G. (1940). The units of group-rings. Proc. London Math. Soc. (2) 46:231–248.
  • Hughes, I., Pearson, K. R. (1972). The group of units of the integral group ring ZS3. Canad. Math. Bull. 15:529–534.
  • Kimmerle, W., Konovalov, A. (2013). Recent advances on torsion subgroups of integral group rings. Proc. Groups St Andrews 2013 422:331–347.
  • Luthar, I.S., Passi, I. B. S. (1989). Zassenhaus conjecture for A5. Proc. Indian Acad. Sci. Math. Sci. 99(1):1–5.
  • Luthar, I. S., Trama, P. (1991). Zassenhaus conjecture for S5. Comm. Algebra 19(8):2353–2362.
  • Margolis, L. (2015). Torsion units in integral group rings of non-solvable groups. Ph.D. Thesis–Stuttgart. http://dx.doi.org/10.18419/opus-5172.
  • Margolis, L. (2016). A Sylow theorem for the integral group ring of PSL(2,q). J. Algebra 445:295–306.
  • Margolis, L., del Rio, Á., Serrano, M. (2016). Zassenhaus Conjecture on torsion units holds for PSL(2,p) with p a Fermat or Mersenne prime. 32 pages. http://arxiv.org/abs/1608.05797.
  • Marciniak, Z., Ritter, J., Sehgal, S. K., Weiss, A. (1987). Torsion units in integral group rings of some metabelian groups. II. J. Number Theory 25(3):340–352.
  • Sehgal, S. K. (1993). Units in Integral Group Rings, volume 69 of Pitman Monographs and Surveys in Pure and Applied Mathematics. Harlow: Longman Scientific & Technical.
  • Serre, J.-P. (1978). Linear representations of finite groups, revised edition. Paris: Hermann.
  • Srinivasan, B. (1964). On the modular characters of the special linear group SL(2, pn). Proc. London Math. Soc. (3) 14:101–114.
  • Wagner, R. (1995). Zassenhaus Conjecture about the groups PSL(2,p). Master thesis, University of Stuttgart. Diplomarbeit Universitat Stuttgart.
  • Weiss, A. (1991). Torsion units in integral group rings. J. Reine Angew. Math. 415:175–187.

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