TY - JOUR
T1 - A solution to Brauer's Problem 14
AU - Murray, John
AU - Sambale, Benjamin
N1 - Funding Information:
The paper was written while the first author visited the University of Hannover in November 2022. Both authors thank Burkhard Külshammer for some interesting discussion on the subject. Also Rod Gow and an anonymous referee made some valuable suggestions to improve the paper. The second author is supported by the German Research Foundation ( SA 2864/4-1 ).
PY - 2023/5/1
Y1 - 2023/5/1
N2 - It is well known that the number of real irreducible characters of a finite group G coincides with the number of real conjugacy classes of G. Richard Brauer has asked if the number of irreducible characters with Frobenius–Schur indicator 1 can also be expressed in group theoretical terms. We show that this can done by counting solutions of g12…gn2=1 with g1,…,gn∈G.
AB - It is well known that the number of real irreducible characters of a finite group G coincides with the number of real conjugacy classes of G. Richard Brauer has asked if the number of irreducible characters with Frobenius–Schur indicator 1 can also be expressed in group theoretical terms. We show that this can done by counting solutions of g12…gn2=1 with g1,…,gn∈G.
KW - Brauer's Problem 14
KW - Frobenius–Schur indicator
KW - Real characters
UR - http://www.scopus.com/inward/record.url?scp=85147556633&partnerID=8YFLogxK
U2 - 10.48550/arXiv.2212.08357
DO - 10.48550/arXiv.2212.08357
M3 - Article
AN - SCOPUS:85147556633
VL - 621
SP - 87
EP - 91
JO - Journal of algebra
JF - Journal of algebra
SN - 0021-8693
ER -