Details
| Original language | English |
|---|---|
| Pages (from-to) | 601-628 |
| Number of pages | 28 |
| Journal | Algebra and Number Theory |
| Volume | 9 |
| Issue number | 3 |
| Publication status | Published - 17 Apr 2015 |
Abstract
We prove that the double covers of the alternating and symmetric groups are determined by their complex group algebras. To be more precise, let n ≥ 5 be an integer, G a finite group, and let Ân and Ŝ±ndenote the double covers of An and Ŝn, respectively. We prove that (formula presented) if and only if (formula presented), and (formula presented) if and only if (formula presented). This in particular completes the proof of a conjecture proposed by the second and fourth authors that every finite quasisimple group is determined uniquely up to isomorphism by the structure of its complex group algebra. The known results on prime power degrees and relatively small degrees of irreducible (linear and projective) representations of the symmetric and alternating groups together with the classification of finite simple groups play an essential role in the proofs.
Keywords
- Alternating groups, Character degrees, Complex group algebras, Double covers, Irreducible representations, Schur covers, Symmetric groups
ASJC Scopus subject areas
- Mathematics(all)
- Algebra and Number Theory
Cite this
- Standard
- Harvard
- Apa
- Vancouver
- BibTeX
- RIS
In: Algebra and Number Theory, Vol. 9, No. 3, 17.04.2015, p. 601-628.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Complex group algebras of the double covers of the symmetric and alternating groups
AU - Bessenrodt, Christine
AU - Nguyen, Hung Ngoc
AU - Olsson, Jørn B.
AU - Tong-Viet, Hung P.
PY - 2015/4/17
Y1 - 2015/4/17
N2 - We prove that the double covers of the alternating and symmetric groups are determined by their complex group algebras. To be more precise, let n ≥ 5 be an integer, G a finite group, and let Ân and Ŝ±ndenote the double covers of An and Ŝn, respectively. We prove that (formula presented) if and only if (formula presented), and (formula presented) if and only if (formula presented). This in particular completes the proof of a conjecture proposed by the second and fourth authors that every finite quasisimple group is determined uniquely up to isomorphism by the structure of its complex group algebra. The known results on prime power degrees and relatively small degrees of irreducible (linear and projective) representations of the symmetric and alternating groups together with the classification of finite simple groups play an essential role in the proofs.
AB - We prove that the double covers of the alternating and symmetric groups are determined by their complex group algebras. To be more precise, let n ≥ 5 be an integer, G a finite group, and let Ân and Ŝ±ndenote the double covers of An and Ŝn, respectively. We prove that (formula presented) if and only if (formula presented), and (formula presented) if and only if (formula presented). This in particular completes the proof of a conjecture proposed by the second and fourth authors that every finite quasisimple group is determined uniquely up to isomorphism by the structure of its complex group algebra. The known results on prime power degrees and relatively small degrees of irreducible (linear and projective) representations of the symmetric and alternating groups together with the classification of finite simple groups play an essential role in the proofs.
KW - Alternating groups
KW - Character degrees
KW - Complex group algebras
KW - Double covers
KW - Irreducible representations
KW - Schur covers
KW - Symmetric groups
UR - http://www.scopus.com/inward/record.url?scp=84936945014&partnerID=8YFLogxK
U2 - 10.2140/ant.2015.9.601
DO - 10.2140/ant.2015.9.601
M3 - Article
AN - SCOPUS:84936945014
VL - 9
SP - 601
EP - 628
JO - Algebra and Number Theory
JF - Algebra and Number Theory
SN - 1937-0652
IS - 3
ER -