Local functions on finite groups

Isaacs, I.; Navarro, Gabriel

doi:10.1090/ert/535

Local functions on finite groups
HTML articles powered by AMS MathViewer

by I. M. Isaacs and Gabriel Navarro PDF

Represent. Theory 24 (2020), 1-37 Request permission

Abstract:

We study local properties of finite groups using chains of $p$-subgroups.

References

J. L. Alperin, Weights for finite groups, The Arcata Conference on Representations of Finite Groups (Arcata, Calif., 1986) Proc. Sympos. Pure Math., vol. 47, Amer. Math. Soc., Providence, RI, 1987, pp. 369–379. MR 933373
Richard Brauer, Investigations on group characters, Ann. of Math. (2) 42 (1941), 936–958. MR 5731, DOI 10.2307/1968775
Kenneth S. Brown, Euler characteristics of groups: the $p$-fractional part, Invent. Math. 29 (1975), no. 1, 1–5. MR 385008, DOI 10.1007/BF01405170
Kenneth S. Brown, High dimensional cohomology of discrete groups, Proc. Nat. Acad. Sci. U.S.A. 73 (1976), no. 6, 1795–1797. MR 419682, DOI 10.1073/pnas.73.6.1795
E. C. Dade, Blocks with cyclic defect groups, Ann. of Math. (2) 84 (1966), 20–48. MR 200355, DOI 10.2307/1970529
Everett C. Dade, Counting characters in blocks. I, Invent. Math. 109 (1992), no. 1, 187–210. MR 1168370, DOI 10.1007/BF01232023
I. Martin Isaacs, Character theory of finite groups, Dover Publications, Inc., New York, 1994. Corrected reprint of the 1976 original [Academic Press, New York; MR0460423 (57 #417)]. MR 1280461
I. Martin Isaacs, Finite group theory, Graduate Studies in Mathematics, vol. 92, American Mathematical Society, Providence, RI, 2008. MR 2426855, DOI 10.1090/gsm/092
I. Martin Isaacs, Characters of solvable groups, Graduate Studies in Mathematics, vol. 189, American Mathematical Society, Providence, RI, 2018. MR 3791517, DOI 10.1090/gsm/189
Radha Kessar and Markus Linckelmann, Dade’s ordinary conjecture implies the Alperin-McKay conjecture, Arch. Math. (Basel) 112 (2019), no. 1, 19–25. MR 3901898, DOI 10.1007/s00013-018-1230-9
Reinhard Knörr and Geoffrey R. Robinson, Some remarks on a conjecture of Alperin, J. London Math. Soc. (2) 39 (1989), no. 1, 48–60. MR 989918, DOI 10.1112/jlms/s2-39.1.48
Burkhard Külshammer and Geoffrey R. Robinson, On Alperin’s conjecture and certain subgroup complexes, Algebr. Represent. Theory 1 (1998), no. 4, 383–398. MR 1683619, DOI 10.1023/A:1009961408896
G. Navarro, Characters and blocks of finite groups, London Mathematical Society Lecture Note Series, vol. 250, Cambridge University Press, Cambridge, 1998. MR 1632299, DOI 10.1017/CBO9780511526015
Gabriel Navarro, Character theory and the McKay conjecture, Cambridge Studies in Advanced Mathematics, vol. 175, Cambridge University Press, Cambridge, 2018. MR 3753712, DOI 10.1017/9781108552790
Daniel Quillen, Homotopy properties of the poset of nontrivial $p$-subgroups of a group, Adv. in Math. 28 (1978), no. 2, 101–128. MR 493916, DOI 10.1016/0001-8708(78)90058-0
Geoffrey R. Robinson, Local structure, vertices and Alperin’s conjecture, Proc. London Math. Soc. (3) 72 (1996), no. 2, 312–330. MR 1367081, DOI 10.1112/plms/s3-72.2.312
Jacques Thévenaz, Locally determined functions and Alperin’s conjecture, J. London Math. Soc. (2) 45 (1992), no. 3, 446–468. MR 1180255, DOI 10.1112/jlms/s2-45.3.446
P. J. Webb, Subgroup complexes, The Arcata Conference on Representations of Finite Groups (Arcata, Calif., 1986) Proc. Sympos. Pure Math., vol. 47, Amer. Math. Soc., Providence, RI, 1987, pp. 349–365. MR 933372, DOI 10.1016/0022-4049(82)90103-7
Thomas R. Wolf, Variations on McKay’s character degree conjecture, J. Algebra 135 (1990), no. 1, 123–138. MR 1076081, DOI 10.1016/0021-8693(90)90153-F