Books

book cover

Endliche Permutationsgruppen, Springer Spektrum, Wiesbaden, 2017, errata,
MAGMA code for Bem 8.28,
GAP code for Bem 8.28,
GAP code for Satz 10.23,
GAP code for Satz 11.3

book cover

Blocks of finite groups and their invariants, Lecture Notes in Math. 2127, Springer-Verlag, Cham, 2014,
pdf (Habilitation thesis), errata
Caution: pdf file has different numbering than actual book,

book cover

2-Blöcke mit metazyklischen und minimal nichtabelschen Defektgruppen,
Südwestdeutscher Verlag für Hochschulschriften, Saarbrücken, 2011,
pdf (Dissertation)

Research articles (in reverse chronological order)

The pdf files contain the most recent version of the paper.

  1. (with P. Diaconis, E. Giannelli, R. M. Guralnick, S. Law, G. Navarro and H. Spink) On the number and sizes of double cosets of Sylow subgroups of the symmetric group, submitted, pdf
  2. Characterizing inner automorphisms and realizing outer automorphisms, appears in Adv. Group Theory Appl., pdf
  3. Fusion invariant characters of \(p\)-groups, Comm. Algebra 53 (2025), 2328–2332, pdf
  4. (with S. Koshitani and C. Lassueur) Principal 2-blocks with wreathed defect groups up to splendid Morita equivalence, Ann. Rep. Theory 1 (2024), 439–463, pdf
  5. On a fixed point formula of Navarro-Rizo, Proc. Amer. Math. Soc. 152 (2024), 3629–3634, pdf
  6. (with P. J. Cameron, D. Craven, H. R. Dorbidi and S. Harper) Minimal cover groups, J. Algebra 660 (2024), 345–372, pdf
  7. (with P. Bhowal, P. J. Cameron and R. K. Nath) Genus and crosscap of solvable conjugacy class graphs of finite groups, Arch. Math. 122 (2024), 475–489, pdf
  8. Real characters in nilpotent blocks, Vietnam J. Math. 52 (2024, special issue), 421–433, pdf
  9. On redundant Sylow subgroups, J. Algebra 650 (2024), 1–9, pdf
  10. (with S. Aivazidis and M. Loukaki) Common transversals and complements in abelian groups, J. Algebraic Combin. 59 (2024), 581–595, pdf
  11. Groups of \(p\)-central type, Math. Z. 306 (2024), no. 3, pdf
  12. (with D. Benson) Finite dimensional algebras not arising as blocks of group algebras, Forum Math. 36 (2024), 389–402, pdf
  13. Real blocks with dihedral defect groups revisited, Bull. Aust. Math. Soc. 109 (2024), 327–341, pdf
  14. (with N. N. Hung and P. H. Tiep) Bounding \(p\)-Brauer characters in finite groups with two conjugacy classes of \(p\)-elements, Israel J. Math. 262 (2024), 327–358, pdf
  15. On the converse of Gaschütz' complement theorem, J. Group Theory 26 (2023), 931–949, pdf (improved version)
  16. Character table sudokus, Arch. Math. 121 (2023), 23–32, pdf
  17. (with A. Moretó) Groups with 2-generated Sylow subgroups and their character tables, Pacific J. Math. 323 (2023), 337–358, pdf
  18. (with G. Navarro) Characters, Commutators and Centers of Sylow Subgroups, Represent. Theory 27 (2023), 717–733, pdf
  19. (with P. Bhowal, P. J. Cameron and R. K. Nath) Solvable conjugacy class graph of groups, Discrete Math. 346 (2023), 113467, pdf
  20. (with J. Murray) A solution to Brauer's Problem 14, J. Algebra 621 (2023), 87–91 , pdf
  21. An invitation to formal power series, Jahresber. Dtsch. Math.-Ver. 125 (2023), 3–69, pdf (improved version)
  22. (with G. Navarro) Alternating sums over \(\pi\)-subgroups, J. Pure Appl. Algebra 227 (2023), 107227, pdf
  23. (with C. G. Ardito) Cartan matrices and Brauer's \(k(B)\)-Conjecture V, J. Algebra 606 (2022), 670–699, pdf
  24. (with P. Wellmann) On a bound of Cocke and Venkataraman, Monatsh. Math. 197 (2022), 505–515, pdf, small group ids
  25. (with M. Tărnăuceanu) On the size of coset unions, J. Algebraic Combin., 55 (2022), 979–987, pdf
  26. (with S. Koshitani and C. Lassueur) Splendid Morita equivalences for principal blocks with semidihedral defect groups, Proc. Amer. Math. Soc., 150 (2022), 41–53, pdf
  27. (with C. G. Ardito) Broué's Conjecture for 2-blocks with elementary abelian defect groups of order 32, Adv. Group Theory Appl. 12 (2021), 71–78, pdf
  28. (with D. Rossi) Restrictions of characters in p-solvable groups, J. Algebra 587 (2021), 130–141, pdf
  29. The reciprocal character of the conjugation action, Publ. Math. Debrecen 99 (2021), 243–260, pdf
  30. Generalized bases of finite groups, Arch. Math. 117 (2021), 9–18, pdf
  31. Blocks with small-dimensional basic algebra, Bull. Aust. Math. Soc., 103 (2021), 461–474, pdf
  32. (with G. Navarro) Weights and nilpotent subgroups, Int. Math. Res. Not. 2021 (2021), 2526–2538, pdf
  33. Survey on perfect isometries, Rocky Mountain J. Math. 50 (2020), 1517–1539, pdf
  34. On a theorem of Ledermann and Neumann, Amer. Math. Monthly 127 (2020), 827–834, pdf
  35. (with E. Giannelli, N. Rizo and A. A. Schaeffer Fry) Groups with few \(p'\)-characters degrees in the principal block, Proc. Amer. Math. Soc. 148 (2020), 4597–4614, pdf
  36. Character tables and defect groups, J. Algebra 562 (2020), 323–340, pdf
  37. (with E. Giannelli) On restriction of characters to defect groups, J. Algebra 558 (2020), 423–433, pdf
  38. (with A. Bächle) Orders generated by character values, Monatsh. Math. 191 (2020), 665–678, pdf
  39. Landau's Theorem for \(\pi\)-blocks of \(\pi\)-separable groups, Adv. Group Theory Appl. 8 (2019), 103–115, pdf
  40. (with I. M. Isaacs and G. Navarro) Irreducible extensions of characters, Israel J. Math. 234 (2019), 629–644, pdf
  41. Bounding the number of characters in a block of a finite group, Adv. Math. 358 (2019), 106861, 20 pp., pdf
  42. Pseudo Frobenius numbers, Expo. Math. 37 (2019), 200–206, pdf
  43. (with B. Külshammer and Y. Otokita) Loewy lengths of centers of blocks II, Nagoya Math. J. 234 (2019), 127–138, pdf
  44. Pseudo Sylow numbers, Amer. Math. Monthly 126 (2019), 60–65, pdf
  45. On the projective height zero conjecture, Proc. Amer. Math. Soc. 147 (2019), 487–488, pdf
  46. Morita equivalent blocks of symmetric groups, SIGMA 14 (2018), 100, 8 pages, GAP code for Conjecture 1, GAP code for Conjecture 2, Magma code for Conjecture 2
  47. Remarks on Harada's Conjecture, Israel J. Math. 228 (2018), 513–526, pdf
  48. (with B. Külshammer) Loewy lengths of centers of blocks, Q. J. Math. 69 (2018), 855–870, pdf
  49. (with G. Navarro) On the blockwise modular isomorphism problem, Manuscripta Math. 157 (2018), 263–278, pdf
  50. (with A. Bächle) Groups whose elements are not conjugate to their powers, Arch. Math. 110 (2018), 447–454, pdf
  51. Solution of Brauer's \(k(B)\)-Conjecture for \(\pi\)-blocks of \(\pi\)-separable groups, Forum Math. 30 (2018), 1061–1064, pdf
  52. (with G. Navarro and P. H. Tiep) Characters and Sylow 2-subgroups of maximal class revisited, J. Pure Appl. Algebra 222 (2018), 3721–3732, pdf
  53. Regular orbits of coprime linear groups in large characteristic, Bull. Aust. Math. Soc. 96 (2017), 438–444, pdf
  54. A counterexample to a conjecture of Wada, J. Algebra 489 (2017), 582–585, pdf
  55. (with G. Malle and G. Navarro) On defects of characters and decomposition numbers, Algebra Number Theory 11 (2017), 1357–1384, pdf
  56. Refinements of the orthogonality relations for blocks, Algebr. Represent. Theory 20 (2017), 1109–1131, pdf
  57. On a theorem of Blichfeldt, Expo. Math. 35 (2017), 221–255, pdf
  58. Isotypies for the quasisimple groups with exceptional Schur multiplier, J. Algebra Appl. 16 (2017), 1750078, pdf
  59. Cartan matrices and Brauer's \(k(B)\)-Conjecture IV, J. Math. Soc. Japan 69 (2017), 735–754, pdf
  60. (with G. Navarro) A counterexample to Feit's Problem VIII on decomposition numbers, J. Algebra 477 (2017), 494–495, pdf
  61. On blocks with abelian defect groups of small rank, Results Math. 71 (2017), 411–422, pdf
  62. (with P. Landrock) On centers of blocks with one simple module, J. Algebra 472 (2017), 339–368, pdf
  63. Fusion systems on bicyclic 2-groups, Proc. Edinb. Math. Soc. 59 (2016), 989–1018, pdf
  64. 2-Blocks with minimal nonabelian defect groups III, Pacific J. Math. 280 (2016), 475–487, pdf
  65. Broué's isotypy conjecture for the sporadic groups and their covers and automorphism groups, Internat. J. Algebra Comput. 25 (2015), 951–976, pdf
  66. The Alperin-McKay Conjecture for metacyclic, minimal non-abelian defect groups, Proc. Amer. Math. Soc. 143 (2015), 4291–4304, pdf
  67. Cartan matrices and Brauer's \(k(B)\)-Conjecture III, Manuscripta Math. 146 (2015), 505–518, pdf
  68. (with L. Héthelyi, R. Kessar and B. Külshammer) Blocks with transitive fusion systems, J. Algebra 424 (2015), 190–207, pdf
  69. Exponent and \(p\)-rank of finite \(p\)-groups and applications, Arch. Math. (Basel) 103 (2014), 11–20, pdf
  70. (with S. Koshitani and B. Külshammer) On Loewy lengths of blocks, Math. Proc. Cambridge Philos. Soc. 156 (2014), 555–570, pdf
  71. (with B. Külshammer, G. Navarro and P. H. Tiep) Finite groups with two conjugacy classes of p-elements and related questions for p-blocks, Bull. London Math. Soc. 46 (2014), 305–314, pdf
  72. On the Brauer-Feit bound for abelian defect groups, Math. Z. 276 (2014), 785–797, pdf
  73. (with C. W. Eaton, R. Kessar and B. Külshammer) 2-blocks with abelian defect groups, Adv. Math. 254 (2014), 706–735, pdf
  74. (with L. Héthelyi and B. Külshammer) A note on Olsson's Conjecture, J. Algebra 398 (2014), 364–385, pdf
  75. Further evidence for conjectures in block theory, Algebra Number Theory 7 (2013), 2241–2273, pdf
  76. Blocks with defect group \(Q_{2^n}\times C_{2^m}\) and \(SD_{2^n}\times C_{2^m}\), Algebr. Represent. Theory 16 (2013), 1717–1732, pdf
  77. Blocks with central product defect group \(D_{2^n}*C_{2^m}\), Proc. Amer. Math. Soc. 141 (2013), 4057–4069, pdf
  78. Brauer's Height Zero Conjecture for metacyclic defect groups, Pacific J. Math. 262 (2013), 481–507, pdf
  79. (with B. Külshammer) The 2-blocks of defect 4, Represent. Theory 17 (2013), 226–236, pdf
  80. (with C. W. Eaton and B. Külshammer) 2-Blocks with minimal nonabelian defect groups II, J. Group Theory 15 (2012), 311–321, pdf
  81. Blocks with defect group \(D_{2^n}\times C_{2^m}\), J. Pure Appl. Algebra 216 (2012), 119–125, pdf
  82. Fusion systems on metacyclic 2-groups, Osaka J. Math. 49 (2012), 325–329, pdf
  83. 2-Blocks with minimal nonabelian defect groups, J. Algebra 337 (2011), 261–284, pdf
  84. Cartan matrices and Brauer's \(k(B)\)-conjecture II, J. Algebra 337 (2011), 345–362, pdf
  85. Cartan matrices and Brauer's \(k(B)\)-conjecture, J. Algebra 331 (2011), 416–427, pdf
  86. (with L. Héthelyi and B. Külshammer) Conjugacy classes and characters of finite p-groups, Comm. Algebra 39 (2011), 657–685, pdf

Other writings

Some of my papers are also on arXiv.

If you find any mistakes/typos, please let me know.

\[l(G)=\sum_{P}\mu(P)k^0(\mathrm{N}_G(P)/P)\]