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More on automorphism groups of laminated near-rings

Published online by Cambridge University Press:  20 January 2009

D. K. Blevins ,
K. D. Magill Jr ,
P. R. Misra ,
J. C. Parnami  and
U. B. Tewari
D. K. Blevins
Affiliation:
Epistemos, Inc. Quaker Hill, Connecticut 06375, U.S.A.
K. D. Magill Jr
Affiliation:
College of Staten Island, Staten Island, New York 10301, U.S.A.
P. R. Misra
Affiliation:
IIT Kanpur, Kanpur-208016, U.P., India
J. C. Parnami
Affiliation:
SUNY at Buffalo, Buffalo, New York 14214–3093, U.S.A.
U. B. Tewari
Affiliation:
Punjab University, Chandigarh 160014, India
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We will assume throughout this paper that polynomials are nonconstant. Let P be any complex polynomial and let p denote the near-ring of all continuous selfmaps of the complex plane where addition of functions is pointwise and multiplication is defined by fg = f ο P ο g for all f,g∈p. The near-ring p is referred to as a laminated near-ring and P is referred to as the laminating element or laminator. In [1] the problem was posed of determining Aut p the automorphism group of p. It was shown that exactly three infinite groups occur as automorphism groups of the laminated near-rings p and for each of the three groups those polynomials P were characterized such that Aut p is isomorphic to that particular group. The infinite groups turn out to be GL(2), the full linear group of all 2×2 nonsingular real matrices and two of its subgroups.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 31 , Issue 2 , June 1988 , pp. 185 - 195
Copyright
Copyright © Edinburgh Mathematical Society 1988

References

REFERENCES

1.Magill, K. D., Misra, P. R. and Tewari, U. B., Automorphism groups of laminated near-rings determined by complex polynomials, Proc. Edinburgh Math. Soc. 26 (1983), 73–84.CrossRefGoogle Scholar
2.Magill, K. D., Misra, P. R. and Tewari, U. B., Finite automorphism groups of laminated near-rings, Proc. Edinburgh Math. Soc. 26 (1983), 297–306.CrossRefGoogle Scholar
3.Walsh, J. L., The Location of Critical Points of Analytic and Harmonic Functions (Colloquium Pub. Vol. 34, Amer. Math. Soc., New York, 1950).Google Scholar