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 M. Schwiering, T. Ziegler, L. Binkowski) Exhaustive, feasible parametrisation with applications to the travelling salesperson problem, submitted, pdf
  2. (with G. Navarro) A counterexample to a conjecture of A. R. Miller, appears in Enseign. Math., pdf
  3. (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, J. Algebra 689 (2026), 62–86, pdf
  4. Fusion invariant characters of \(p\)-groups, Comm. Algebra 53 (2025), 2328–2332, pdf
  5. Characterizing inner automorphisms and realizing outer automorphisms, Adv. Group Theory Appl. 22 (2025), 155–175, pdf
  6. (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
  7. On a fixed point formula of Navarro-Rizo, Proc. Amer. Math. Soc. 152 (2024), 3629–3634, pdf
  8. (with P. J. Cameron, D. Craven, H. R. Dorbidi and S. Harper) Minimal cover groups, J. Algebra 660 (2024), 345–372, pdf
  9. (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
  10. Real characters in nilpotent blocks, Vietnam J. Math. 52 (2024, special issue), 421–433, pdf
  11. On redundant Sylow subgroups, J. Algebra 650 (2024), 1–9, pdf
  12. (with S. Aivazidis and M. Loukaki) Common transversals and complements in abelian groups, J. Algebraic Combin. 59 (2024), 581–595, pdf
  13. Groups of \(p\)-central type, Math. Z. 306 (2024), no. 3, pdf
  14. (with D. Benson) Finite dimensional algebras not arising as blocks of group algebras, Forum Math. 36 (2024), 389–402, pdf
  15. Real blocks with dihedral defect groups revisited, Bull. Aust. Math. Soc. 109 (2024), 327–341, pdf
  16. (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
  17. On the converse of Gaschütz' complement theorem, J. Group Theory 26 (2023), 931–949, pdf (improved version)
  18. Character table sudokus, Arch. Math. 121 (2023), 23–32, pdf
  19. (with A. Moretó) Groups with 2-generated Sylow subgroups and their character tables, Pacific J. Math. 323 (2023), 337–358, pdf
  20. (with G. Navarro) Characters, Commutators and Centers of Sylow Subgroups, Represent. Theory 27 (2023), 717–733, pdf
  21. (with P. Bhowal, P. J. Cameron and R. K. Nath) Solvable conjugacy class graph of groups, Discrete Math. 346 (2023), 113467, pdf
  22. (with J. Murray) A solution to Brauer's Problem 14, J. Algebra 621 (2023), 87–91 , pdf
  23. An invitation to formal power series, Jahresber. Dtsch. Math.-Ver. 125 (2023), 3–69, pdf (improved version)
  24. (with G. Navarro) Alternating sums over \(\pi\)-subgroups, J. Pure Appl. Algebra 227 (2023), 107227, pdf
  25. (with C. G. Ardito) Cartan matrices and Brauer's \(k(B)\)-Conjecture V, J. Algebra 606 (2022), 670–699, pdf
  26. (with P. Wellmann) On a bound of Cocke and Venkataraman, Monatsh. Math. 197 (2022), 505–515, pdf, small group ids
  27. (with M. Tărnăuceanu) On the size of coset unions, J. Algebraic Combin., 55 (2022), 979–987, pdf
  28. (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
  29. (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
  30. (with D. Rossi) Restrictions of characters in p-solvable groups, J. Algebra 587 (2021), 130–141, pdf
  31. The reciprocal character of the conjugation action, Publ. Math. Debrecen 99 (2021), 243–260, pdf
  32. Generalized bases of finite groups, Arch. Math. 117 (2021), 9–18, pdf
  33. Blocks with small-dimensional basic algebra, Bull. Aust. Math. Soc., 103 (2021), 461–474, pdf
  34. (with G. Navarro) Weights and nilpotent subgroups, Int. Math. Res. Not. 2021 (2021), 2526–2538, pdf
  35. Survey on perfect isometries, Rocky Mountain J. Math. 50 (2020), 1517–1539, pdf
  36. On a theorem of Ledermann and Neumann, Amer. Math. Monthly 127 (2020), 827–834, pdf
  37. (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
  38. Character tables and defect groups, J. Algebra 562 (2020), 323–340, pdf
  39. (with E. Giannelli) On restriction of characters to defect groups, J. Algebra 558 (2020), 423–433, pdf
  40. (with A. Bächle) Orders generated by character values, Monatsh. Math. 191 (2020), 665–678, pdf
  41. Landau's Theorem for \(\pi\)-blocks of \(\pi\)-separable groups, Adv. Group Theory Appl. 8 (2019), 103–115, pdf
  42. (with I. M. Isaacs and G. Navarro) Irreducible extensions of characters, Israel J. Math. 234 (2019), 629–644, pdf
  43. Bounding the number of characters in a block of a finite group, Adv. Math. 358 (2019), 106861, 20 pp., pdf
  44. Pseudo Frobenius numbers, Expo. Math. 37 (2019), 200–206, pdf
  45. (with B. Külshammer and Y. Otokita) Loewy lengths of centers of blocks II, Nagoya Math. J. 234 (2019), 127–138, pdf
  46. Pseudo Sylow numbers, Amer. Math. Monthly 126 (2019), 60–65, pdf
  47. On the projective height zero conjecture, Proc. Amer. Math. Soc. 147 (2019), 487–488, pdf
  48. 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
  49. Remarks on Harada's Conjecture, Israel J. Math. 228 (2018), 513–526, pdf
  50. (with B. Külshammer) Loewy lengths of centers of blocks, Q. J. Math. 69 (2018), 855–870, pdf
  51. (with G. Navarro) On the blockwise modular isomorphism problem, Manuscripta Math. 157 (2018), 263–278, pdf
  52. (with A. Bächle) Groups whose elements are not conjugate to their powers, Arch. Math. 110 (2018), 447–454, pdf
  53. Solution of Brauer's \(k(B)\)-Conjecture for \(\pi\)-blocks of \(\pi\)-separable groups, Forum Math. 30 (2018), 1061–1064, pdf
  54. (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
  55. Regular orbits of coprime linear groups in large characteristic, Bull. Aust. Math. Soc. 96 (2017), 438–444, pdf
  56. A counterexample to a conjecture of Wada, J. Algebra 489 (2017), 582–585, pdf
  57. (with G. Malle and G. Navarro) On defects of characters and decomposition numbers, Algebra Number Theory 11 (2017), 1357–1384, pdf
  58. Refinements of the orthogonality relations for blocks, Algebr. Represent. Theory 20 (2017), 1109–1131, pdf
  59. On a theorem of Blichfeldt, Expo. Math. 35 (2017), 221–255, pdf
  60. Isotypies for the quasisimple groups with exceptional Schur multiplier, J. Algebra Appl. 16 (2017), 1750078, pdf
  61. Cartan matrices and Brauer's \(k(B)\)-Conjecture IV, J. Math. Soc. Japan 69 (2017), 735–754, pdf
  62. (with G. Navarro) A counterexample to Feit's Problem VIII on decomposition numbers, J. Algebra 477 (2017), 494–495, pdf
  63. On blocks with abelian defect groups of small rank, Results Math. 71 (2017), 411–422, pdf
  64. (with P. Landrock) On centers of blocks with one simple module, J. Algebra 472 (2017), 339–368, pdf
  65. Fusion systems on bicyclic 2-groups, Proc. Edinb. Math. Soc. 59 (2016), 989–1018, pdf
  66. 2-Blocks with minimal nonabelian defect groups III, Pacific J. Math. 280 (2016), 475–487, pdf
  67. Broué's isotypy conjecture for the sporadic groups and their covers and automorphism groups, Internat. J. Algebra Comput. 25 (2015), 951–976, pdf
  68. The Alperin-McKay Conjecture for metacyclic, minimal non-abelian defect groups, Proc. Amer. Math. Soc. 143 (2015), 4291–4304, pdf
  69. Cartan matrices and Brauer's \(k(B)\)-Conjecture III, Manuscripta Math. 146 (2015), 505–518, pdf
  70. (with L. Héthelyi, R. Kessar and B. Külshammer) Blocks with transitive fusion systems, J. Algebra 424 (2015), 190–207, pdf
  71. Exponent and \(p\)-rank of finite \(p\)-groups and applications, Arch. Math. (Basel) 103 (2014), 11–20, pdf
  72. (with S. Koshitani and B. Külshammer) On Loewy lengths of blocks, Math. Proc. Cambridge Philos. Soc. 156 (2014), 555–570, pdf
  73. (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
  74. On the Brauer-Feit bound for abelian defect groups, Math. Z. 276 (2014), 785–797, pdf
  75. (with C. W. Eaton, R. Kessar and B. Külshammer) 2-blocks with abelian defect groups, Adv. Math. 254 (2014), 706–735, pdf
  76. (with L. Héthelyi and B. Külshammer) A note on Olsson's Conjecture, J. Algebra 398 (2014), 364–385, pdf
  77. Further evidence for conjectures in block theory, Algebra Number Theory 7 (2013), 2241–2273, pdf
  78. 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
  79. Blocks with central product defect group \(D_{2^n}*C_{2^m}\), Proc. Amer. Math. Soc. 141 (2013), 4057–4069, pdf
  80. Brauer's Height Zero Conjecture for metacyclic defect groups, Pacific J. Math. 262 (2013), 481–507, pdf
  81. (with B. Külshammer) The 2-blocks of defect 4, Represent. Theory 17 (2013), 226–236, pdf
  82. (with C. W. Eaton and B. Külshammer) 2-Blocks with minimal nonabelian defect groups II, J. Group Theory 15 (2012), 311–321, pdf
  83. Blocks with defect group \(D_{2^n}\times C_{2^m}\), J. Pure Appl. Algebra 216 (2012), 119–125, pdf
  84. Fusion systems on metacyclic 2-groups, Osaka J. Math. 49 (2012), 325–329, pdf
  85. 2-Blocks with minimal nonabelian defect groups, J. Algebra 337 (2011), 261–284, pdf
  86. Cartan matrices and Brauer's \(k(B)\)-conjecture II, J. Algebra 337 (2011), 345–362, pdf
  87. Cartan matrices and Brauer's \(k(B)\)-conjecture, J. Algebra 331 (2011), 416–427, pdf
  88. (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.

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