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FACTORIZATION NUMBERS OF SOME FINITE GROUPS

Published online by Cambridge University Press:  12 December 2011

F. SAEEDI  and
M. FARROKHI D. G.
F. SAEEDI
Affiliation:
Department of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, Iran. e-mail: [email protected]
M. FARROKHI D. G.
Affiliation:
Department of Pure Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran. e-mail: [email protected]
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Abstract

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For a finite group G, let F2(G) be the number of factorizations G = AB of the group G, where A and B are subgroups of G. We compute F2(G) for certain classes of groups, including cyclic groups ℤn, elementary abelian p-groups ℤpn, dihedral groups D2n, generalised quaternion groups Q4n, quasi-dihedral 2-groups QD2n(n≥4), modular p-groups Mpn, projective general linear groups PGL(2, pn) and projective special linear groups PSL(2, pn).

Keywords

Primary 20D40secondary 20P05
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 54 , Issue 2 , May 2012 , pp. 345 - 354
Copyright
Copyright © Glasgow Mathematical Journal Trust 2011

References

REFERENCES

1.Blaum, M., Factorizations of the simple groups PSL 3(q) and PSU 3(q 2), Arch. Math. 40 (1983), 8–13.CrossRefGoogle Scholar
2.Gentchev, T. R., Factorizations of the sporadic simple groups, Arch. Math. 47 (1986), 97–102.CrossRefGoogle Scholar
3.Gentchev, T. R., Factorizations of the groups of Lie type of Lie rank 1 or 2, Arch. Math. 47 (1986), 493–499.CrossRefGoogle Scholar
4.Huppert, B., Endliche Gruppen I (Springer-Verlag, Berlin, 1967).CrossRefGoogle Scholar
5.Ito, N., On the factorizations of the linear fractional group LF(2, pn), Acta Sci. Math. (Szeged), 15 (1953), 79–84.Google Scholar
6.Tchakerian, K. B. and Gentchev, T. R., Factorizations of the groups G 2(q), Arch. Math. 44 (1985), 230–232.CrossRefGoogle Scholar
7.Tărnăuceanu, M., Subgroup commutativity degrees of finite groups, J. Algebra 321 (9) (2009), 2508–2520.CrossRefGoogle Scholar
8.The GAP Group, GAP Algorithms and Programming, Version 4.4.12 (2008), http://www.gap-system.org/Google Scholar