- -

Itô's theorem on groups with two class sizes revisited

RiuNet: Institutional repository of the Polithecnic University of Valencia

Share/Send to

Cited by

Statistics

Itô's theorem on groups with two class sizes revisited

Show full item record

Alemany Martínez, E.; Beltrán, A.; Felipe Román, MJ. (2012). Itô's theorem on groups with two class sizes revisited. Bulletin of the Australian Mathematical Society. 85:476-481. doi:10.1017/S0004972711002875

Por favor, use este identificador para citar o enlazar este ítem: http://hdl.handle.net/10251/31896

Files in this item

[Cerrado]
Name: baz53173-offprint ...
Size: 98.53Kb
Format: PDF
Description: Versión editorial
Request a copy of the document

Item Metadata

Title: Itô's theorem on groups with two class sizes revisited
Author: Alemany Martínez, Elena Beltrán, Antonio Felipe Román, María Josefa
UPV Unit: Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada
Universitat Politècnica de València. Instituto Universitario de Matemática Pura y Aplicada - Institut Universitari de Matemàtica Pura i Aplicada
Issued date:
Abstract:
Let G be a finite p-solvable group. We prove that if G has exactly two conjugacy class sizes of p'-elements of prime power order, say 1 and m, then m = p(a)q(b), for two distinct primes p and q, and G either has an abelian ...[+]
Subjects: Finite groups , Conjugacy class sizes , Solvable groups
Copyrigths: Cerrado
Source:
Bulletin of the Australian Mathematical Society. (issn: 0004-9727 ) (eissn: 1755-1633 )
DOI: 10.1017/S0004972711002875
Publisher:
Cambridge University Press
Publisher version: http://dx.doi.org/10.1017/S0004972711002875
Project ID:
Spanish Government, Proyecto [MTM2010-19938-C03-02]
Valencian Government, Proyecto [PROMETEO/2011/30]
Fundacio Caixa-Castello [P11B2010-47]
Thanks:
This research is supported by the Spanish Government, Proyecto MTM2010-19938-C03-02 and the second and third authors are supported by the Valencian Government, Proyecto PROMETEO/2011/30. The second author is also supported ...[+]
Type: Artículo

References

Huppert, B. (1998). Character Theory of Finite Groups. doi:10.1515/9783110809237

Baer, R. (1953). Group elements of prime power index. Transactions of the American Mathematical Society, 75(1), 20-20. doi:10.1090/s0002-9947-1953-0055340-0

Kurzweil, H., & Stellmacher, B. (2004). The Theory of Finite Groups. Universitext. doi:10.1007/b97433 [+]
Huppert, B. (1998). Character Theory of Finite Groups. doi:10.1515/9783110809237

Baer, R. (1953). Group elements of prime power index. Transactions of the American Mathematical Society, 75(1), 20-20. doi:10.1090/s0002-9947-1953-0055340-0

Kurzweil, H., & Stellmacher, B. (2004). The Theory of Finite Groups. Universitext. doi:10.1007/b97433

Beltrán, A., & Felipe, M. J. (2003). Finite groups with two p-regular conjugacy class lengths. Bulletin of the Australian Mathematical Society, 67(1), 163-169. doi:10.1017/s000497270003361x

Camina, A. R. (1974). Finite groups of conjugate rank 2. Nagoya Mathematical Journal, 53, 47-57. doi:10.1017/s0027763000016019

Zhao, X., & Guo, X. (2009). On Conjugacy Class Sizes of the p′-Elements with Prime Power Order. Algebra Colloquium, 16(04), 541-548. doi:10.1142/s1005386709000510

Shirong, L. (1996). Finite groups with exactly two class lengths of elements of prime power order. Archiv der Mathematik, 67(2), 100-105. doi:10.1007/bf01268923

Itô, N. (1953). On Finite Groups with Given Conjugate Types I. Nagoya Mathematical Journal, 6, 17-28. doi:10.1017/s0027763000016937

Camina, R. D., & Camina, A. R. (1998). Implications of conjugacy class size. Journal of Group Theory, 1(3). doi:10.1515/jgth.1998.017

Beltrán, A., & Felipe, M. J. (2004). Prime powers as conjugacy class lengths of π-elements. Bulletin of the Australian Mathematical Society, 69(2), 317-325. doi:10.1017/s0004972700036054

[-]

This item appears in the following Collection(s)

Show full item record