Details
| Original language | English |
|---|---|
| Pages (from-to) | 665-678 |
| Number of pages | 14 |
| Journal | Monatshefte fur Mathematik |
| Volume | 191 |
| Issue number | 4 |
| Early online date | 23 Aug 2019 |
| Publication status | Published - Apr 2020 |
| Externally published | Yes |
Abstract
Let K: = Q(G) be the number field generated by the complex character values of a finite group G. Let ZK be the ring of integers of K. In this paper we investigate the suborder Z[G] of ZK generated by the character values of G. We prove that every prime divisor of the order of the finite abelian group ZK/ Z[G] divides |G|. Moreover, if G is nilpotent, we show that the exponent of ZK/ Z[G] is a proper divisor of |G| unless G= 1. We conjecture that this holds for arbitrary finite groups G.
Keywords
- Algebraic integers, Field of character values, Finite groups, Orders
ASJC Scopus subject areas
- Mathematics(all)
- General Mathematics
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In: Monatshefte fur Mathematik, Vol. 191, No. 4, 04.2020, p. 665-678.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Orders generated by character values
AU - Bächle, Andreas
AU - Sambale, Benjamin
N1 - Funding information: The work on this paper started with a visit of the first author at the University of Jena in January 2019. He appreciates the hospitality received there. The authors also like to thank Thomas Breuer for making them aware of the CoReLG package [ 2 ] of GAP [ 11 ] which was used for computations with alternating groups. The first author is a postdoctoral researcher of the FWO (Research Foundation Flanders). The second author is supported by the German Research Foundation (SA 2864/1-1 and SA 2864/3-1). The work on this paper started with a visit of the first author at the University of Jena in January 2019. He appreciates the hospitality received there. The authors also like to thank Thomas Breuer for making them aware of the CoReLG package?[2] of GAP?[11] which was used for computations with alternating groups. The first author is a postdoctoral researcher of the FWO (Research Foundation Flanders). The second author is supported by the German Research Foundation (SA 2864/1-1 and SA 2864/3-1).
PY - 2020/4
Y1 - 2020/4
N2 - Let K: = Q(G) be the number field generated by the complex character values of a finite group G. Let ZK be the ring of integers of K. In this paper we investigate the suborder Z[G] of ZK generated by the character values of G. We prove that every prime divisor of the order of the finite abelian group ZK/ Z[G] divides |G|. Moreover, if G is nilpotent, we show that the exponent of ZK/ Z[G] is a proper divisor of |G| unless G= 1. We conjecture that this holds for arbitrary finite groups G.
AB - Let K: = Q(G) be the number field generated by the complex character values of a finite group G. Let ZK be the ring of integers of K. In this paper we investigate the suborder Z[G] of ZK generated by the character values of G. We prove that every prime divisor of the order of the finite abelian group ZK/ Z[G] divides |G|. Moreover, if G is nilpotent, we show that the exponent of ZK/ Z[G] is a proper divisor of |G| unless G= 1. We conjecture that this holds for arbitrary finite groups G.
KW - Algebraic integers
KW - Field of character values
KW - Finite groups
KW - Orders
UR - http://www.scopus.com/inward/record.url?scp=85071315020&partnerID=8YFLogxK
U2 - 10.1007/s00605-019-01324-3
DO - 10.1007/s00605-019-01324-3
M3 - Article
AN - SCOPUS:85071315020
VL - 191
SP - 665
EP - 678
JO - Monatshefte fur Mathematik
JF - Monatshefte fur Mathematik
SN - 0026-9255
IS - 4
ER -