Details
| Originalsprache | Englisch |
|---|---|
| Seiten (von - bis) | 657-685 |
| Seitenumfang | 29 |
| Fachzeitschrift | Communications in algebra |
| Jahrgang | 39 |
| Ausgabenummer | 2 |
| Publikationsstatus | Veröffentlicht - Feb. 2011 |
| Extern publiziert | Ja |
Abstract
Let K be a conjugacy class of a finite p-group G where p is a prime, and let K-1 denote the conjugacy class of G consisting of the inverses of the elements in K. We observe that, in several cases, the number of elements in the product KK-1 is congruent to 1 modulo p -1, and we pose the question in which generality this congruence is valid. We also consider related properties of the class multiplication constants of G. Furthermore, let χ be an irreducible character of G, and let χ- denote the complex conjugate of χ. We show that, in several cases, the number of irreducible constituents of the product χχ- is congruent to 1 modulo p -1, and we pose the question in which generality this congruence is valid.
ASJC Scopus Sachgebiete
- Mathematik (insg.)
- Algebra und Zahlentheorie
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in: Communications in algebra, Jahrgang 39, Nr. 2, 02.2011, S. 657-685.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - Conjugacy classes and characters of finite p-groups
AU - Héthelyi, Lászlo
AU - Külshammer, Burkhard
AU - Sambale, Benjamin
N1 - Funding Information: The authors are grateful to J. Schmidt [14] for providing GAP files containing the groups of order 37 and 57. Also, the first named author was supported by an OTKA grant (National Scientific Research Grant No. T049841).
PY - 2011/2
Y1 - 2011/2
N2 - Let K be a conjugacy class of a finite p-group G where p is a prime, and let K-1 denote the conjugacy class of G consisting of the inverses of the elements in K. We observe that, in several cases, the number of elements in the product KK-1 is congruent to 1 modulo p -1, and we pose the question in which generality this congruence is valid. We also consider related properties of the class multiplication constants of G. Furthermore, let χ be an irreducible character of G, and let χ- denote the complex conjugate of χ. We show that, in several cases, the number of irreducible constituents of the product χχ- is congruent to 1 modulo p -1, and we pose the question in which generality this congruence is valid.
AB - Let K be a conjugacy class of a finite p-group G where p is a prime, and let K-1 denote the conjugacy class of G consisting of the inverses of the elements in K. We observe that, in several cases, the number of elements in the product KK-1 is congruent to 1 modulo p -1, and we pose the question in which generality this congruence is valid. We also consider related properties of the class multiplication constants of G. Furthermore, let χ be an irreducible character of G, and let χ- denote the complex conjugate of χ. We show that, in several cases, the number of irreducible constituents of the product χχ- is congruent to 1 modulo p -1, and we pose the question in which generality this congruence is valid.
KW - Character
KW - Conjugacy class
UR - http://www.scopus.com/inward/record.url?scp=79951974958&partnerID=8YFLogxK
U2 - 10.1080/00927871003598723
DO - 10.1080/00927871003598723
M3 - Article
AN - SCOPUS:79951974958
VL - 39
SP - 657
EP - 685
JO - Communications in algebra
JF - Communications in algebra
SN - 0092-7872
IS - 2
ER -