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  • F. SAEEDI (a1) and M. FARROKHI D. G. (a2)

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).

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1.M. Blaum , Factorizations of the simple groups PSL3(q) and PSU3(q2), Arch. Math. 40 (1983), 813.

2.T. R. Gentchev , Factorizations of the sporadic simple groups, Arch. Math. 47 (1986), 97102.

3.T. R. Gentchev , Factorizations of the groups of Lie type of Lie rank 1 or 2, Arch. Math. 47 (1986), 493499.

4.B. Huppert , Endliche Gruppen I (Springer-Verlag, Berlin, 1967).

6.K. B. Tchakerian and T. R. Gentchev , Factorizations of the groups G2(q), Arch. Math. 44 (1985), 230232.

7.M. Tărnăuceanu , Subgroup commutativity degrees of finite groups, J. Algebra 321 (9) (2009), 25082520.

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Glasgow Mathematical Journal
  • ISSN: 0017-0895
  • EISSN: 1469-509X
  • URL: /core/journals/glasgow-mathematical-journal
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