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The order of groups satisfying a converse to Lagrange's theorem

  • Naihuan Jing (a1)


One of the converse statements to Lagrange's theorem is that, for each subgroup H of G and any prime factor p of |G: H|, there exists a subgroup K such that H≤K≤G with |K: H | = p. This paper treats integers n such that all groups of order n have this property.



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[Bl]Bechtell, H.. Theory of Groups (Addison-Wesley, 1971).
[B2]Berger, T. R.. A converse to Lagrange's theorem. J. Austral. Math. Soc., 25 (1978), 291313.
[BW]Bray, H. G., Deskins, W. E., Johnson, D., Humphreys, J. F., Puttaswamaiah, M., Venzke, P., Walls, G. L. and Weinstein, M.. Between nilpotent and solvable (Polygonal Publishing House, Passaic, 1982).
[FZ]Fan, Y. and Zhang, Y. D.. On supersolubility of groups of order n. Jour. Math. (Wuhan), 1 (1981), 8695.
[H]Huppert, B.. Endliche Gruppen I (Springer-Verlag, Berlin, Heidelberg, New York, 1967).
[Ml]McCarthy, D. J.. A survey of partial converses to Lagrange's theorem on finite groups. Trans. New York Acad. Sci. (2), 33 (1971), 586594.
[M2]McLain, D. H.. The existence of subgroups of given order in finite groups. Proc. Cambridge Philos. Soc., 53 (1957), 278285.
[PI]Pazderski, G.. Die Ordnungen, zu denen nur Gruppen mit gegebener Eigenschaft gehören. Arch. Math., 10 (1959), 331343.
[P2]Pazderski, G.. The orders of which only belong to metabelian groups. Math. Nachr., 95 (1980), 716.
[SI]Struik, R. R.. Partial converses to Lagrange's theorem. Commun. Alg. 6(5) (1978), 421482.
[S2]Struik, R. R.. Partial converses to Lagrange's theorem II. Commun. Alg., 9(1) (1981), 122.
[Z]Zhang, Y. D.. An outline of supersolvable groups. Adv. in Math. (Beijing), 11 (1982), 200205.
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  • ISSN: 0025-5793
  • EISSN: 2041-7942
  • URL: /core/journals/mathematika
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