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Cyclicity conditions for division algebras of prime degree
Author(s):
M.
Mahdavi-Hezavehi;
J.-P.
Tignol
Journal:
Proc. Amer. Math. Soc.
131
(2003),
3673-3676.
MSC (2000):
Primary 16K20
Posted:
February 26, 2003
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Abstract:
Let  be a division algebra of prime degree  . A set of criteria is given for cyclicity of  in terms of subgroups of the multiplicative group  of  . It is essentially shown that  is cyclic if and only if  contains a nonabelian metabelian subgroup.
References:
-
- 1.
- S. A. Amitsur, Finite subgroups of division rings, Trans. Amer. Math. Soc., 80 (1955), 361-386. MR 17:577c
- 2.
- P. K. Draxl, Skew fields, LMS Lecture Note Series, No. 81, Cambridge University Press, (1982). MR 85a:16022
- 3.
- I. N. Herstein, Finite multiplicative subgroups in division rings, Pacific J. Math. 3 (1953), 121-126. MR 14:1056j
- 4.
- Hua Loo-Keng, Some properties of a field, Proc. Nat. Acad. Sci. U.S.A. 35 (1949), 533-537. MR 11:155c
- 5.
- Hua Loo-Keng, On the multiplicative group of a field, Acad. Sinica Science Record 3 (1950), 1-6 (English, Chinese summary). MR 12:584e
- 6.
- M. S. Huzurbazar, The multiplicative group of a division ring, Dokl. Akad. Nauk SSSR 131 (1960), 1268-1271 = Soviet Math. Dokl. 1 (1960), 433-435. MR 22:11009
- 7.
- M. Mahdavi-Hezavehi, Free subgroups in maximal subgroups of
 , J. Algebra 241 (2001), 720-730. MR 2002c:16023 - 8.
- W. R. Scott, On the multiplicative group of a division ring, Proc. Amer. Math. Soc. 8 (1957), 303-305. MR 18:788g
- 9.
- J.-P. Tignol, Sur les décompositions des algèbres à division en produit tensoriel d'algèbres cycliques, in Brauer groups in ring theory and algebraic geometry (F. van Oystaeyen and A. Verschoren, eds), Lecture Notes in Math. 917, Springer-Verlag, Berlin, 1982, pp. 126-145. MR 83i:16020
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Additional Information:
M.
Mahdavi-Hezavehi
Affiliation:
Department of Mathematical Sciences, Sharif University of Technology, P. O. Box 11365--9415, Tehran, Iran
Email:
mahdavih@sharif.edu
J.-P.
Tignol
Affiliation:
Institut de Mathématique Pure et Appliquée, Université Catholique de Louvain, 1348 Louvain-la-Neuve, Belgium
Email:
tignol@math.ucl.ac.be
DOI:
10.1090/S0002-9939-03-06959-4
PII:
S 0002-9939(03)06959-4
Received by editor(s):
June 19, 2002
Received by editor(s) in revised form:
July 15, 2002
Posted:
February 26, 2003
Additional Notes:
The first author thanks the Research Council of Sharif University of Technology for support. He also thanks Professor J.-P. Tignol for his hospitality during his stay at the Université Catholique de Louvain in May 2002.
The second author was partially supported by the National Fund for Scientific Research (Belgium).
Communicated by:
Martin Lorenz
Copyright of article:
Copyright
2003,
American Mathematical Society
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