Solution of the Hughes problem for finite $p$-groups of class $2p-2$.
HTML articles powered by AMS MathViewer
- by I. D. Macdonald PDF
- Proc. Amer. Math. Soc. 27 (1971), 39-42 Request permission
Abstract:
In this paper the Hughes conjecture for finite $p$-groups is proved in the case of groups which are nilpotent of class $2p - 2$.References
- Warren Brisley, On varieties of metabelian $p$-groups, and their laws, J. Austral Math. Soc. 7 (1967), 64β80. MR 0207832, DOI 10.1017/S1446788700005103
- N. D. Gupta and M. F. Newman, On metabelian groups, J. Austral. Math. Soc. 6 (1966), 362β368. MR 0202835, DOI 10.1017/S1446788700004316
- Marshall Hall Jr., The theory of groups, The Macmillan Company, New York, N.Y., 1959. MR 0103215
- C. R. Hobby, Nearly regular $p$-groups, Canadian J. Math. 19 (1967), 520β522. MR 215922, DOI 10.4153/CJM-1967-044-8
- Guy T. Hogan and Wolfgang P. Kappe, On the $H_{p}$-problem for finite $p$-groups, Proc. Amer. Math. Soc. 20 (1969), 450β454. MR 238952, DOI 10.1090/S0002-9939-1969-0238952-8 D. R. Hughes, A problem in group theory, Bull. Amer. Math. Soc. 63 (1957), 209.
- D. R. Hughes and J. G. Thompson, The $H$-problem and the structure of $H$-groups, Pacific J. Math. 9 (1959), 1097β1101. MR 108532, DOI 10.2140/pjm.1959.9.1097
- I. D. Macdonald, The Hughes problem and others, J. Austral. Math. Soc. 10 (1969), 475β479. MR 0254143, DOI 10.1017/S1446788700007746
- H. Meier-Wunderli, Metabelsche Gruppen, Comment. Math. Helv. 25 (1951), 1β10 (German). MR 40296, DOI 10.1007/BF02566442
- E. G. Straus and G. Szekeres, On a problem of D. R. Hughes, Proc. Amer. Math. Soc. 9 (1958), 157β158. MR 93549, DOI 10.1090/S0002-9939-1958-0093549-0
- G. E. Wall, On Hughesβ $H_{p}$ problem, Proc. Internat. Conf. Theory of Groups (Canberra, 1965) Gordon and Breach, New York, 1967, pp.Β 357β362. MR 0219607
- Guido Zappa, Contributo allo studio del studio del problema di Hughes sui gruppi, Ann. Mat. Pura Appl. (4) 57 (1962), 211β219 (Italian, with English summary). MR 137761, DOI 10.1007/BF02417738
Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 27 (1971), 39-42
- MSC: Primary 20.40
- DOI: https://doi.org/10.1090/S0002-9939-1971-0271230-9
- MathSciNet review: 0271230