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 S. Aivazidis) Groups satisfying Gaschütz's complement theorem, submitted, pdf
  2. (with M. Schwiering, T. Ziegler, L. Binkowski) Exhaustive, feasible parametrisation with applications to the travelling salesperson problem, appears in Proc. IEEE Quantum Week 2026 (QCE26), pdf
  3. (with G. Navarro) A counterexample to a conjecture of A. R. Miller, appears in Enseign. Math., pdf
  4. (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
  5. Fusion invariant characters of \(p\)-groups, Comm. Algebra 53 (2025), 2328–2332, pdf
  6. Characterizing inner automorphisms and realizing outer automorphisms, Adv. Group Theory Appl. 22 (2025), 155–175, pdf
  7. (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
  8. On a fixed point formula of Navarro-Rizo, Proc. Amer. Math. Soc. 152 (2024), 3629–3634, pdf
  9. (with P. J. Cameron, D. Craven, H. R. Dorbidi and S. Harper) Minimal cover groups, J. Algebra 660 (2024), 345–372, pdf
  10. (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
  11. Real characters in nilpotent blocks, Vietnam J. Math. 52 (2024, special issue), 421–433, pdf
  12. On redundant Sylow subgroups, J. Algebra 650 (2024), 1–9, pdf
  13. (with S. Aivazidis and M. Loukaki) Common transversals and complements in abelian groups, J. Algebraic Combin. 59 (2024), 581–595, pdf
  14. Groups of \(p\)-central type, Math. Z. 306 (2024), no. 3, pdf
  15. (with D. Benson) Finite dimensional algebras not arising as blocks of group algebras, Forum Math. 36 (2024), 389–402, pdf
  16. Real blocks with dihedral defect groups revisited, Bull. Aust. Math. Soc. 109 (2024), 327–341, pdf
  17. (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
  18. On the converse of Gaschütz' complement theorem, J. Group Theory 26 (2023), 931–949, pdf (improved version)
  19. Character table sudokus, Arch. Math. 121 (2023), 23–32, pdf
  20. (with A. Moretó) Groups with 2-generated Sylow subgroups and their character tables, Pacific J. Math. 323 (2023), 337–358, pdf
  21. (with G. Navarro) Characters, Commutators and Centers of Sylow Subgroups, Represent. Theory 27 (2023), 717–733, pdf
  22. (with P. Bhowal, P. J. Cameron and R. K. Nath) Solvable conjugacy class graph of groups, Discrete Math. 346 (2023), 113467, pdf
  23. (with J. Murray) A solution to Brauer's Problem 14, J. Algebra 621 (2023), 87–91 , pdf
  24. An invitation to formal power series, Jahresber. Dtsch. Math.-Ver. 125 (2023), 3–69, pdf (improved version)
  25. (with G. Navarro) Alternating sums over \(\pi\)-subgroups, J. Pure Appl. Algebra 227 (2023), 107227, pdf
  26. (with C. G. Ardito) Cartan matrices and Brauer's \(k(B)\)-Conjecture V, J. Algebra 606 (2022), 670–699, pdf
  27. (with P. Wellmann) On a bound of Cocke and Venkataraman, Monatsh. Math. 197 (2022), 505–515, pdf, small group ids
  28. (with M. Tărnăuceanu) On the size of coset unions, J. Algebraic Combin., 55 (2022), 979–987, pdf
  29. (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
  30. (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
  31. (with D. Rossi) Restrictions of characters in p-solvable groups, J. Algebra 587 (2021), 130–141, pdf
  32. The reciprocal character of the conjugation action, Publ. Math. Debrecen 99 (2021), 243–260, pdf
  33. Generalized bases of finite groups, Arch. Math. 117 (2021), 9–18, pdf
  34. Blocks with small-dimensional basic algebra, Bull. Aust. Math. Soc., 103 (2021), 461–474, pdf
  35. (with G. Navarro) Weights and nilpotent subgroups, Int. Math. Res. Not. 2021 (2021), 2526–2538, pdf
  36. Survey on perfect isometries, Rocky Mountain J. Math. 50 (2020), 1517–1539, pdf
  37. On a theorem of Ledermann and Neumann, Amer. Math. Monthly 127 (2020), 827–834, pdf
  38. (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
  39. Character tables and defect groups, J. Algebra 562 (2020), 323–340, pdf
  40. (with E. Giannelli) On restriction of characters to defect groups, J. Algebra 558 (2020), 423–433, pdf
  41. (with A. Bächle) Orders generated by character values, Monatsh. Math. 191 (2020), 665–678, pdf
  42. Landau's Theorem for \(\pi\)-blocks of \(\pi\)-separable groups, Adv. Group Theory Appl. 8 (2019), 103–115, pdf
  43. (with I. M. Isaacs and G. Navarro) Irreducible extensions of characters, Israel J. Math. 234 (2019), 629–644, pdf
  44. Bounding the number of characters in a block of a finite group, Adv. Math. 358 (2019), 106861, 20 pp., pdf
  45. Pseudo Frobenius numbers, Expo. Math. 37 (2019), 200–206, pdf
  46. (with B. Külshammer and Y. Otokita) Loewy lengths of centers of blocks II, Nagoya Math. J. 234 (2019), 127–138, pdf
  47. Pseudo Sylow numbers, Amer. Math. Monthly 126 (2019), 60–65, pdf
  48. On the projective height zero conjecture, Proc. Amer. Math. Soc. 147 (2019), 487–488, pdf
  49. 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
  50. Remarks on Harada's Conjecture, Israel J. Math. 228 (2018), 513–526, pdf
  51. (with B. Külshammer) Loewy lengths of centers of blocks, Q. J. Math. 69 (2018), 855–870, pdf
  52. (with G. Navarro) On the blockwise modular isomorphism problem, Manuscripta Math. 157 (2018), 263–278, pdf
  53. (with A. Bächle) Groups whose elements are not conjugate to their powers, Arch. Math. 110 (2018), 447–454, pdf
  54. Solution of Brauer's \(k(B)\)-Conjecture for \(\pi\)-blocks of \(\pi\)-separable groups, Forum Math. 30 (2018), 1061–1064, pdf
  55. (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
  56. Regular orbits of coprime linear groups in large characteristic, Bull. Aust. Math. Soc. 96 (2017), 438–444, pdf
  57. A counterexample to a conjecture of Wada, J. Algebra 489 (2017), 582–585, pdf
  58. (with G. Malle and G. Navarro) On defects of characters and decomposition numbers, Algebra Number Theory 11 (2017), 1357–1384, pdf
  59. Refinements of the orthogonality relations for blocks, Algebr. Represent. Theory 20 (2017), 1109–1131, pdf
  60. On a theorem of Blichfeldt, Expo. Math. 35 (2017), 221–255, pdf
  61. Isotypies for the quasisimple groups with exceptional Schur multiplier, J. Algebra Appl. 16 (2017), 1750078, pdf
  62. Cartan matrices and Brauer's \(k(B)\)-Conjecture IV, J. Math. Soc. Japan 69 (2017), 735–754, pdf
  63. (with G. Navarro) A counterexample to Feit's Problem VIII on decomposition numbers, J. Algebra 477 (2017), 494–495, pdf
  64. On blocks with abelian defect groups of small rank, Results Math. 71 (2017), 411–422, pdf
  65. (with P. Landrock) On centers of blocks with one simple module, J. Algebra 472 (2017), 339–368, pdf
  66. Fusion systems on bicyclic 2-groups, Proc. Edinb. Math. Soc. 59 (2016), 989–1018, pdf
  67. 2-Blocks with minimal nonabelian defect groups III, Pacific J. Math. 280 (2016), 475–487, pdf
  68. Broué's isotypy conjecture for the sporadic groups and their covers and automorphism groups, Internat. J. Algebra Comput. 25 (2015), 951–976, pdf
  69. The Alperin-McKay Conjecture for metacyclic, minimal non-abelian defect groups, Proc. Amer. Math. Soc. 143 (2015), 4291–4304, pdf
  70. Cartan matrices and Brauer's \(k(B)\)-Conjecture III, Manuscripta Math. 146 (2015), 505–518, pdf
  71. (with L. Héthelyi, R. Kessar and B. Külshammer) Blocks with transitive fusion systems, J. Algebra 424 (2015), 190–207, pdf
  72. Exponent and \(p\)-rank of finite \(p\)-groups and applications, Arch. Math. (Basel) 103 (2014), 11–20, pdf
  73. (with S. Koshitani and B. Külshammer) On Loewy lengths of blocks, Math. Proc. Cambridge Philos. Soc. 156 (2014), 555–570, pdf
  74. (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
  75. On the Brauer-Feit bound for abelian defect groups, Math. Z. 276 (2014), 785–797, pdf
  76. (with C. W. Eaton, R. Kessar and B. Külshammer) 2-blocks with abelian defect groups, Adv. Math. 254 (2014), 706–735, pdf
  77. (with L. Héthelyi and B. Külshammer) A note on Olsson's Conjecture, J. Algebra 398 (2014), 364–385, pdf
  78. Further evidence for conjectures in block theory, Algebra Number Theory 7 (2013), 2241–2273, pdf
  79. 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
  80. Blocks with central product defect group \(D_{2^n}*C_{2^m}\), Proc. Amer. Math. Soc. 141 (2013), 4057–4069, pdf
  81. Brauer's Height Zero Conjecture for metacyclic defect groups, Pacific J. Math. 262 (2013), 481–507, pdf
  82. (with B. Külshammer) The 2-blocks of defect 4, Represent. Theory 17 (2013), 226–236, pdf
  83. (with C. W. Eaton and B. Külshammer) 2-Blocks with minimal nonabelian defect groups II, J. Group Theory 15 (2012), 311–321, pdf
  84. Blocks with defect group \(D_{2^n}\times C_{2^m}\), J. Pure Appl. Algebra 216 (2012), 119–125, pdf
  85. Fusion systems on metacyclic 2-groups, Osaka J. Math. 49 (2012), 325–329, pdf
  86. 2-Blocks with minimal nonabelian defect groups, J. Algebra 337 (2011), 261–284, pdf
  87. Cartan matrices and Brauer's \(k(B)\)-conjecture II, J. Algebra 337 (2011), 345–362, pdf
  88. Cartan matrices and Brauer's \(k(B)\)-conjecture, J. Algebra 331 (2011), 416–427, pdf
  89. (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.

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