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Groups of prime-power order

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1456)

Keywords

  • Maximal Class
  • Nilpotency Class
  • Isomorphism Type
  • Elementary Abelian Group
  • Lower Central Series

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References

  • Judith A. Ascione, George Havas and C.R. Leedham-Green (1977), ‘A computer aided classification of certain groups of prime power order’, Bull. Austral. Math. Soc. 17, 257–274. Corrigendum: 317–319. Microfiche supplement: 320.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • Judith A. Ascione (1979), On 3-groups of second maximal class, Ph.D. thesis, Australian National University.

    Google Scholar 

  • G. Bagnera (1898), ‘La composizione dei Gruppi finiti il cui grado è la quinta potenza di un numero primo’, Ann. Mat. Pura Appl. (3) 1, 137–228.

    CrossRef  Google Scholar 

  • N. Blackburn (1958), ‘On a special class of p-groups’, Acta. Math. 100, 45–92.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • Geoffrey Blainey (1966), The tyranny of distance (Sun Books, Melbourne; also Macmillan, Melbourne, 1968).

    Google Scholar 

  • W. Burnside (1897), Theory of groups of finite order (Cambridge University Press).

    Google Scholar 

  • John J. Cannon (1984), ‘An introduction to the group theory language, Cayley’, in Computational Group Theory, Proceedings, Durham, 1982; ed. by Michael D. Atkinson, pp. 145–183 (Academic Press, London, New York).

    Google Scholar 

  • A. Cayley (1854), ‘On the theory of groups, as depending on the symbolic equation ϑn=1’, Philos. Mag. (4) 7, 40–47. Mathematical Papers, II, 123–130.

    Google Scholar 

  • A. Cayley (1859), ‘On the theory of groups, as depending on the symbolic equation ϑn=1. Part III’, Philos. Mag. (4) 18, 34–37. Mathematical Papers, IV, 88–91.

    Google Scholar 

  • A. Cayley (1878), ‘Desiderata and suggestions. No. 1. the theory of groups’, Amer. J. Math. 1, 50–52. Mathematical Papers, X, 401–403.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • J.-A. de Séguier (1904), Théorie des groupes finis. Éléments de la théorie des groupes abstraits (Gauthier-Villars, Paris).

    MATH  Google Scholar 

  • Thomas E. Easterfield (1940), A classification of groups of order p 6, Ph.D. thesis, Cambridge University.

    Google Scholar 

  • Richard K. Guy (1988), ‘The strong law of small numbers’, Amer. Math. Monthly 95, 697–712.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • Marshall Hall, Jr. and James K. Senior (1964), The Groups of Order 2n (n⩽6) (Macmillan, New York).

    MATH  Google Scholar 

  • P. Hall (1933), ‘A contribution to the theory of groups of prime-power order’, Proc. London Math. Soc. 36 (1934), 29–95. Collected Works, 59–125.

    MathSciNet  MATH  Google Scholar 

  • P. Hall (1940), ‘The classification of prime-power groups’, J. Reine Angew. Math. 182, 130–141. Collected Works, 265–276.

    MathSciNet  MATH  Google Scholar 

  • Graham Higman (1960a), ‘Enumerating p-groups. I: Inequalities’, Proc. London Math. Soc. (3) 10, 24–30.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • Graham Higman (1960b), ‘Enumerating p-groups. II: Problems whose solution is PORC’, Proc. London Math. Soc. (3) 10, 566–582.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • Graham Higman (1960c), ‘Enumerating p-groups: III’. One of four lectures delivered as part of a group theory seminar at the University of Chicago in Autumn 1960.

    Google Scholar 

  • Otto Hölder (1893), ‘Die Gruppen der Ordnungen p 3, pq 2, pqr, p 4’, Math. Ann. 43, 301–412.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • Rodney K. James (1968), The Groups of Order p 6 (p⩾3), Ph.D. thesis, University of Sydney.

    Google Scholar 

  • Rodney James (1975), ‘2-groups of almost maximal class’, J. Austral. Math. Soc. Ser. A 19, 343–357.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • Rodney James (1980), ‘The groups of order p 6 (p an odd prime)’, Math. Comput. 34, 613–637.

    MathSciNet  MATH  Google Scholar 

  • Rodney James (1983), ‘2-groups of almost maximal class: corrigendum’, J. Austral. Math. Soc. Ser. A 35, 307.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • Rodney James, M. F. Newman and E. A. O’Brien (1990), ‘The groups of order 128’, J. Algebra 129, 136–158.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • A. M. Küpper (1979), Enumeration of some two-generator groups of prime power order, M.Sc. thesis, Australian National University.

    Google Scholar 

  • C. R. Leedham-Green and Susan McKay (1976), ‘On p-groups of maximal class I’, Quart. J. Math. Oxford (2) 27, 297–311.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • C. R. Leedham-Green and Susan McKay (1978a), ‘On p-groups of maximal class II’, Quart. J. Math. Oxford (2) 29, 175–186.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • C. R. Leedham-Green and Susan McKay (1978b), ‘On p-groups of maximal class III’, Quart. J. Math. Oxford (2) 29, 281–299.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • C. R. Leedham-Green and Susan McKay (1984), ‘On the classification of p-groups of maximal class’, Quart. J. Math. Oxford (2) 35, 293–304.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • C. R. Leedham-Green and M. F. Newman (1980), ‘Space groups and groups of prime-power order I’, Arch. Math. (Basel) 35, 193–202.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • C. R. Leedham-Green and L. H. Soicher (1990), ‘Collection from the left and other strategies’, J. Symbolic Comput. (to appear).

    Google Scholar 

  • Ursula Martin (1986), ‘Almost all p-groups have automorphism group a p-group’, Bull. Amer. Math. Soc. (N.S.) 15, 78–82.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • John McKay (1969), ‘Table errata: The Groups of Order 2n (n⩽6), (Macmillan, New York, 1964) by M. Hall and J. K. Senior’, Math. Comput. 23, 691–692.

    CrossRef  MathSciNet  Google Scholar 

  • G. A. Miller (1896), ‘The regular substitution groups whose order is less than 48’, Quart. J. Math. 28, 232–284.

    MATH  Google Scholar 

  • M. F. Newman (1977), ‘Determination of groups of prime-power order’, in Group Theory, Proceedings, Canberra, 1975; ed. by R. A. Bryce, J. Cossey and M. F. Newman; Lecture Notes in Math. 573, pp. 73–84 (Springer-Verlag, Berlin, Heidelberg, New York).

    CrossRef  Google Scholar 

  • M. F. Newman and E. A. O’Brien (1989), ‘A CAYLEY library for the groups of order dividing 128’, in Group Theory, Proceedings of the Singapore Group Theory Conference held at the National University of Singapore, 1987, ed. by Kai Nah Cheng and Yu Kiang Leong, pp. 437–442 (de Gruyter, Berlin, New York).

    Google Scholar 

  • M. F. Newman and Mingyao Xu (1988), ‘Metacyclic groups of prime-power order’, Adv. in Math. (Beijing) 17, 106–107.

    Google Scholar 

  • E. A. O’Brien (1990), ‘The p-group generation algorithm’, J. Symbolic Comput. (to appear).

    Google Scholar 

  • E. A. O’Brien (1991), ‘The groups of order 256’, J. Algebra (to appear).

    Google Scholar 

  • O. S. Pilyavskaya (1983a), Classification of groups of order p 6 (p>3), VINITI Deposit No. 1877–83.

    Google Scholar 

  • O. S. Pilyavskaya (1983b), ‘Application of matrix problems to the classification of groups of order p 6, p>3’, in Linear algebra and the theory of representations, ed. by Yu. A. Mitropol’skii, pp. 86–99 (Inst. Mat. Akad. Nauk Ukrain. SSR, Kiev).

    Google Scholar 

  • M. Potron (1904a), Les groupes d’ordre p 6, doctoral thesis (Gauthier-Villars, Paris).

    MATH  Google Scholar 

  • M. Potron (1904b), ‘Sur quelques groupes d’ordre p 6’, Bull. Soc. Math. France 32, 296–300.

    MathSciNet  MATH  Google Scholar 

  • Martin Schönert (1989), ‘GAP, groups and programming’, Abstracts Amer. Math. Soc. 10, 34.

    Google Scholar 

  • Otto Schreier (1926), ‘Über die Erweiterung von Gruppen. II’, Abh. Math. Sem. Univ. Hamburg 4, 321–346.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • Michio Suzuki (1986), Group Theory II, Grundlehren Math. Wiss. 248 (Springer-Verlag, Berlin, Heidelberg, New York).

    MATH  Google Scholar 

  • Olga Taussky (1937), ‘A remark on the class field tower’, J. London Math. Soc. 12, 82–85.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • Louis William Tordella (1939), A classification of groups of order p 6, p an odd prime, Ph.D. thesis, University of Illinois, Urbana.

    Google Scholar 

  • Douglas Blaine Tyler (1982), Determination of groups of exponent p and order p 7, Ph.D. dissertation, University of California, Los Angeles.

    Google Scholar 

  • Michael Vaughan-Lee (1990), The restricted Burnside problem, London Math. Soc. Monographs 5 (Clarendon Press, Oxford).

    MATH  Google Scholar 

  • J. W. A. Young (1893), ‘On the determination of groups whose order is a power of a prime’, Amer. J. Math. 15, 124–178.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • David Fredric Wilkinson (1983), An application of computers to groups of prime exponent, Ph.D. thesis, University of Warwick.

    Google Scholar 

  • David Wilkinson (1988), ‘The groups of exponent p and order p 7 (p any prime)’, J. Algebra 118, 109–119.

    CrossRef  MathSciNet  MATH  Google Scholar 

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This lecture is dedicated to Bernhard Neumann. I have learned many things from him; for example, the importance of well-chosen examples.

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Newman, M.F. (1990). Groups of prime-power order. In: Kovács, L.G. (eds) Groups—Canberra 1989. Lecture Notes in Mathematics, vol 1456. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0100730

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  • DOI: https://doi.org/10.1007/BFb0100730

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