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• JOURNAL ARTICLE
  Liebeck MW, Schul G, Shalev A, 2017,

  RAPID GROWTH IN FINITE SIMPLE GROUPS

  , TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, Vol: 369, Pages: 8765-8779, ISSN: 0002-9947
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  • Citations: 1
• JOURNAL ARTICLE
  Gonshaw S, Liebeck MW, O'Brien EA, 2017,

  Unipotent class representatives for finite classical groups

  , JOURNAL OF GROUP THEORY, Vol: 20, Pages: 505-525, ISSN: 1433-5883
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  • Citations: 1
• JOURNAL ARTICLE
  Franchi C, Ivanov AA, Mainardis M, 2017,

  Permutation modules for the symmetric group

  , Proceedings of the American Mathematical Society, Vol: 145, Pages: 3249-3262, ISSN: 0002-9939
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• JOURNAL ARTICLE
  Liebeck MW, 2017,

  Character ratios for finite groups of Lie type, and applications

  , FINITE SIMPLE GROUPS: THIRTY YEARS OF THE ATLAS AND BEYOND, Vol: 694, Pages: 193-208, ISSN: 0271-4132
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  • Citations: 2
• JOURNAL ARTICLE
  Proudfoot N, Schedler T, 2017,

  Poisson–de Rham homology of hypertoric varieties and nilpotent cones

  , Selecta Mathematica, Vol: 23, Pages: 179-202, ISSN: 1022-1824
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• JOURNAL ARTICLE
  Ivanov AA, Franchi C, Mainardis M,

  Standard majorana representations of the symmetric groups

  , Journal of Algebraic Combinatorics, ISSN: 1572-9192

  LetGbe a nite group and letWbe a nitely generatedRG-module with a positive de nite bilinear form (;)W. Assume thatGpermutestransitively a generating setXofWand that (;)Wis constant on eachorbital ofGonX. We show a new method for computing the dimensions ofthe irreducible constituents ofW. Further, we apply that method to Majoranarepresentations of the symmetric groups proving that the symmetric groupSnhas a Majorana representation, in which every permutation of type (2;2) ofSncorresponds to a Majorana axis, if and only ifn≤12

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• JOURNAL ARTICLE
  Liebeck MW, O'Brien EA, 2016,

  RECOGNITION OF FINITE EXCEPTIONAL GROUPS OF LIE TYPE

  , TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, Vol: 368, Pages: 6189-6226, ISSN: 0002-9947
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  • Citations: 1
• JOURNAL ARTICLE
  Franchi C, Ivanov AA, Mainardis M, 2016,

  Standard Majorana representations of the symmetric groups

  , Journal of Algebraic Combinatorics, Vol: 44, Pages: 265-292, ISSN: 0925-9899
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• JOURNAL ARTICLE
  Giudici M, Ivanov AA, Morgan L, Praeger CEet al., 2016,

  A characterisation of weakly locally projective amalgams related to A 16 and the sporadic simple groups M 24 and He

  , Journal of Algebra, Vol: 460, Pages: 340-365, ISSN: 0021-8693
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• JOURNAL ARTICLE
  Liebeck MW, Praeger CE, Saxl J,

  The classification of 3/2-transitive permutation groups and 1/2-transitive linear groups

  , Proceedings of the American Mathematical Society, ISSN: 1088-6826

  A linear group G ≤ GL(V ), where V is a finite vector space, is called 12-transitive if allthe G-orbits on the set of nonzero vectors have the same size. We complete the classificationof all the 12-transitive linear groups. As a consequence we complete the determination of thefinite 32-transitive permutation groups – the transitive groups for which a point-stabilizerhas all its nontrivial orbits of the same size. We also determine the (k +12)-transitive groupsfor integers k ≥ 2.

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