Abstract
In this paper, we prove the existence of an elementα of the group algebra A=ℂF of a free groupF with two generatorsx andy over the field of complex numbersC such that, for any complexa andb for which ¦a¦=¦b¦=1, we haveA ∩ ϑ a,b (α)A=0, where ϑ a,b (α is an automorphism ofA that mapsx,y intoax, by, respectively. Thus, we give a negative answer to question 12.46 of P. A. Linnel from “Kourovka Notebook.”
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References
Kourovka Notebook (Unsolved Problems of the Theory of Groups) [in Russian], 12th ed., Novosibirsk (1992).
M. I. Kargapolov and Yu. I. Merzlyakov,Foundations of the Theory of Groups [in Russian], Nauka, Moscow (1972).
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No.4, pp. 571–572, April, 1995.
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Tushev, A.V. On ideals of the group algebra of a free group of degree of freedom two over the field of complex numbers. Ukr Math J 47, 663–664 (1995). https://doi.org/10.1007/BF01056056
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DOI: https://doi.org/10.1007/BF01056056