Details
| Original language | English |
|---|---|
| Pages (from-to) | 2328-2332 |
| Number of pages | 5 |
| Journal | Communications in algebra |
| Volume | 53 |
| Issue number | 6 |
| Publication status | Published - 24 Dec 2024 |
Abstract
We consider complex characters of a p-group P, which are invariant under a fusion system (Formula presented.) on P. Extending a theorem of Bárcenas–Cantarero to non-saturated fusion systems, we show that the number of indecomposable (Formula presented.) -invariant characters of P is greater or equal than the number of (Formula presented.) -conjugacy classes of P. We further prove that these two quantities coincide whenever (Formula presented.) is realized by a p-solvable group. On the other hand, we observe that this is false for constrained fusion systems in general. Finally, we construct a saturated fusion system with an indecomposable (Formula presented.) -invariant character, which is not a summand of the regular character of P. This disproves a recent conjecture of Cantarero–Combariza.
Keywords
- Fusion systems, invariant characters
ASJC Scopus subject areas
- Mathematics(all)
- Algebra and Number Theory
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In: Communications in algebra, Vol. 53, No. 6, 24.12.2024, p. 2328-2332.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Fusion invariant characters of p-groups
AU - Sambale, Benjamin
N1 - Publisher Copyright: © 2024 The Author(s). Published with license by Taylor & Francis Group, LLC.
PY - 2024/12/24
Y1 - 2024/12/24
N2 - We consider complex characters of a p-group P, which are invariant under a fusion system (Formula presented.) on P. Extending a theorem of Bárcenas–Cantarero to non-saturated fusion systems, we show that the number of indecomposable (Formula presented.) -invariant characters of P is greater or equal than the number of (Formula presented.) -conjugacy classes of P. We further prove that these two quantities coincide whenever (Formula presented.) is realized by a p-solvable group. On the other hand, we observe that this is false for constrained fusion systems in general. Finally, we construct a saturated fusion system with an indecomposable (Formula presented.) -invariant character, which is not a summand of the regular character of P. This disproves a recent conjecture of Cantarero–Combariza.
AB - We consider complex characters of a p-group P, which are invariant under a fusion system (Formula presented.) on P. Extending a theorem of Bárcenas–Cantarero to non-saturated fusion systems, we show that the number of indecomposable (Formula presented.) -invariant characters of P is greater or equal than the number of (Formula presented.) -conjugacy classes of P. We further prove that these two quantities coincide whenever (Formula presented.) is realized by a p-solvable group. On the other hand, we observe that this is false for constrained fusion systems in general. Finally, we construct a saturated fusion system with an indecomposable (Formula presented.) -invariant character, which is not a summand of the regular character of P. This disproves a recent conjecture of Cantarero–Combariza.
KW - Fusion systems
KW - invariant characters
UR - http://www.scopus.com/inward/record.url?scp=85216619495&partnerID=8YFLogxK
U2 - 10.1080/00927872.2024.2439491
DO - 10.1080/00927872.2024.2439491
M3 - Article
VL - 53
SP - 2328
EP - 2332
JO - Communications in algebra
JF - Communications in algebra
SN - 0092-7872
IS - 6
ER -