Hostname: page-component-78c5997874-g7gxr Total loading time: 0 Render date: 2024-11-05T12:13:37.215Z Has data issue: false hasContentIssue false
  • English
  • Français

The group of formal power series under substitution

Part of: Special aspects of infinite or finite groups

Published online by Cambridge University Press:  09 April 2009

D. L. Johnson
D. L. Johnson
Affiliation:
Department of Mathematics, The University of NottinghamNottingham NG7 2RD, England
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

This is a study of formal power series under the binary operation of formal composition from a group-theoretical point of view. Various “large” properties are derived.

MSC classification

Secondary: 20F99: None of the above, but in this section
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 45 , Issue 3 , December 1988 , pp. 296 - 302
Copyright
Copyright © Australian Mathematical Society 1988

References

[1]Baker, I. N., ‘Permutable power series and regular iteration’, J. Austral. Math. Soc. 2 (1961/1962), 265–294.CrossRefGoogle Scholar
[2]Jacobsthal, E., ‘Über vertauschbare Polynome’, Math. Z. 63 (1955), 243–276.CrossRefGoogle Scholar
[3]Joyal, A., ‘Un théorie combinatorie des séries formelles’, Adv. in Math. 42 (1981), 1–82.CrossRefGoogle Scholar
[4]Julia, G., ‘Mémoire sur la permutabilité des fractions rationelles’, Ann. Sci. Ecole Norm. Sup. (3) 39 (1922), 131–215.CrossRefGoogle Scholar
[5]Lausch, H. and Nöbauer, W., Algebra of polynomials (North-Holland, Amsterdam, 1973).Google Scholar
[6]Nichols, W. D., ‘Pointed irreducible bialgebras’, J. Algebra 57 (1979), 64–76.CrossRefGoogle Scholar
[7]Pearl, M. J., Query no. 304, Notices Amer. Math. Soc. 31 (1984), 376.Google Scholar
[8]Ritt, J. F., ‘Prime and composite polynomials’, Trans. Amer. Math. Soc. 23 (1922), 51–66.CrossRefGoogle Scholar
[9]White, S., ‘The group generated by x ↦ x + 1 and x ↦ xp is free’, Preprint, Berkeley 1986.Google Scholar
[10]Zassenhaus, H. J., ‘On a problem of Harvey Friedman’, Comm. Algebra 6 (16) (1978), 1629–1634.CrossRefGoogle Scholar