Article
| Title: | Results related to Huppert's $\rho $-$\sigma $ conjecture (English) |
| Author: | Xu, Xia |
| Author: | Yang, Yong |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 73 |
| Issue: | 4 |
| Year: | 2023 |
| Pages: | 1273-1280 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | We improve a few results related to Huppert's $\rho $-$\sigma $ conjecture. We also generalize a result about the covering number of character degrees to arbitrary finite groups. (English) |
| Keyword: | character degree |
| Keyword: | Huppert's conjecture |
| MSC: | 20C15 |
| DOI: | 10.21136/CMJ.2023.0513-22 |
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| Date available: | 2023-11-23T12:28:13Z |
| Last updated: | 2023-11-27 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/151959 |
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| Reference: | [1] Bellotti, C., Keller, T. M., Trudgian, T. S.: New bounds for numbers of primes in element orders of finite groups.Available at https://arxiv.org/abs/2211.05837 (2022), 6 pages. 10.48550/arXiv.2211.05837 |
| Reference: | [2] Hung, N. N., Yang, Y.: On the prime divisors of element orders.Math. Nachr. 294 (2021), 1905-1911. Zbl 07750808, MR 4371273, 10.1002/mana.202000249 |
| Reference: | [3] Keller, T. M.: A linear bound for $\rho(n)$.J. Algebra 178 (1995), 643-652. Zbl 0859.20014, MR 1359907, 10.1006/jabr.1995.1370 |
| Reference: | [4] Liu, Y.: On covering number of groups with trivial Fitting subgroup.Acta Math. Sin., Engl. Ser. 38 (2022), 1277-1284. Zbl 1495.20003, MR 4454357, 10.1007/s10114-022-0521-z |
| Reference: | [5] Manz, O., Wolf, T. R.: Representations of Solvable Groups.London Mathematical Society Lecture Notes Series 185. Cambridge University Press, Cambridge (1993). Zbl 0928.20008, MR 1261638, 10.1017/CBO9780511525971 |
| Reference: | [6] Moretó, A.: On the number of different prime divisors of element orders.Proc. Am. Math. Soc. 134 (2006), 617-619. Zbl 1090.20018, MR 2180876, 10.1090/S0002-9939-05-08156-6 |
| Reference: | [7] Moretó, A.: Huppert's conjecture for character codegrees.Math. Nachr. 294 (2021), 2232-2236. Zbl 07747386, MR 4371296, 10.1002/mana.202000568 |
| Reference: | [8] Qian, G.: A note on element orders and character codegrees.Arch. Math. 97 (2011), 99-103. Zbl 1232.20014, MR 2820570, 10.1007/s00013-011-0278-6 |
| Reference: | [9] Qian, G., Wang, Y., Wei, H.: Co-degrees of irreducible characters in finite groups.J. Algebra 312 (2007), 946-955. Zbl 1127.20009, MR 1127.20009, 10.1016/j.jalgebra.2006.11.001 |
| Reference: | [10] Shi, W.: Characterization of simple groups using orders and related topics.Adv. Math., Beijing 20 (1991), 135-141. Zbl 0732.20007, MR 1121552 |
| Reference: | [11] Yang, Y.: On analogues of Huppert's conjecture.Bull. Aust. Math. Soc. 104 (2021), 272-277. Zbl 07394393, MR 4308143, 10.1017/S0004972720001409 |
| Reference: | [12] Yang, Y., Qian, G.: The analog of Huppert's conjecture on character codegrees.J. Algebra 478 (2017), 215-219. Zbl 1423.20009, MR 3621669, 10.1016/j.jalgebra.2016.12.017 |
| Reference: | [13] Zhang, J.: Arithmetical conditions on element orders and group structure.Proc. Am. Math. Soc. 123 (1995), 39-44. Zbl 0816.20024, MR 1239809, 10.1090/S0002-9939-1995-1239809-1 |
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