Recognizing Abelian Sylow Subgroups in Finite Groups

REFERENCES

• Aschbacher , M. ( 2000 ). Finite Group Theory, Second Edition . Cambridge : Cambridge Studies in Advanced Mathematics .
   Google Scholar
• Borel , A. , Carter , R. , Curtis , C. W. , Iwahori , N. , Springer , T. A. , Steinberg , R. ( 1986 ). Seminar on Algebraic Groups and Related Finite Groups . Berlin-New York : Springer-Verlag .
   Google Scholar
• Brauer , R. ( 1963 ). Representations of finite groups. In: Lectures on Modern Mathematics, vol. I. Wiley, New York .
   Google Scholar
• Conway , J. H. , Curtis , R. T. , Norton , S. P. , Parker , R. A. , Wilson , R. A. The Atlas of Finite Groups. Oxford: Clarendon Press. Reprinted with corrections in 2004.
   Google Scholar
• Camina , A. , Herzog , M. ( 1980 ). Character tables determine abelian sylow 2-subgroups . Proc. Amer. Math. Soc. 80 ( 3 ): 533 – 535 .
   Web of Science ®Google Scholar
• Gorenstein , D. , Lyons , R. ( 1983 ). The local structure of finite groups of characteristic 2 type. Mem. Amer. Math. Soc.
   Google Scholar
• Gorenstein , D. , Lyons , R. , Solomon , R. ( 1998 ). The Classification of the Finite Simple Groups, Number 3 . Providence : American Mathematical Society .
   Google Scholar
• Karpilovsky , G. ( 1987 ). The Schur Multiplier . New York : Oxford University Press .
   Google Scholar
• Külshammer , B. , Navarro , G. , Sambale , B. , Tiep , P. H. ( 2014 ). Finite groups with two conjugacy classes of p-elements and related questions for p-blocks . Bull. London. Math. Soc. 46 : 305 – 314 .
   Web of Science ®Google Scholar
• Kimmerle , W. , Sandling , R. ( 1995 ). Group theoretic determination of certain sylow and hall subgroups and a resolution of a question of R. Brauer . The Journal of Algebra 171 : 329 – 346 .
   Web of Science ®Google Scholar
• Lou , B. ( 1968 ). The centralizer of a regular unipotent element in a semisimple algebraic group . Bull. Amer. Math. Soc. 74 : 1144 – 1146 .
   Web of Science ®Google Scholar
• Lübeck , F. Elements of order 2 and 3 in exceptional groups of Lie type. http://www.math.rwth-aachen.de/Frank.Luebeck/chev/23elts.html. Last updated 2008.
   Google Scholar
• Malle , G. , Testerman , D. ( 2011 ). Linear Algebraic Groups and Finite Groups of Lie type. Cambridge Studies in Advanced Mathematics .
   Google Scholar
• Navarro , G. , Solomon , R. , Tiep , P. H. ( 2014 ). Abelian Sylow subgroups in a finite group, II. The Journal of Algebra dedicated to A. Seress.
   Google Scholar
• Navarro , G. , Tiep , P. H. ( 2014 ). Abelian Sylow subgroups in a finite group. The Journal of Algebra 519–526 .
   Google Scholar
• Robinson , D. ( 1995 ). A Course in the Theory of Groups . New York : Springer .
   Google Scholar
• Weir , A. J. ( 1955 ). Sylow p-subgroups of the classical groups over finite fields with characteristic prime to p. Proceedings of the American Mathematical Society 6:529–533 .
   Google Scholar
• Wilson , R. A. ( 2009 ). The Finite Simple Groups . London : Springer .
   Google Scholar
• Communicated by P. Tiep.
   Google Scholar