Free subsemigroups in the group of linear transformations of number fields

Sumaryuk Mykhailo Illich ^1,2

¹ Institute of Postgraduate Pedagogical Education of Chernivtsi Region, Chernivtsi, 58000, Ukraine

² Department of Algebra and Informatics, Yuriy Fedkovych Chernivtsi National University, Chernivtsi, 58000, Ukraine

Keywords: free subsemigroups, number fields

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Abstract

We find new sufficient conditions under which the semigroup generated by two linear translations of number fields is a free semigroup.

References

[1] Magnus V., Karras A., Solitaire D. Combinatorial Theory of Groups. Translated from English. - M.: Nauka, 1979. - 456 p.

[2] Oliynik A.S., Sushchansky V.I. Free group of infinite unitriangular matrices // Mat. notes. - 2000. - 67, № 3, - P. 386-391.

[3] Oliynyk A.S. Free groups of automata permutations // Supplements of the NAS of Ukraine. - 1998. - № 7. - P. 40-44.

[4] Oliynik A.S. On free semigroups of automaton transformations / / Mat. notes. - 1998. - 63. - P. 248-259.

[5] Sanov I.N. Property of one representation of a free group. - Reports of the USSR Academy of Sciences. - 1947. - 57. - P. 657-659.

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ACS Style: Sumaryuk, M.I. Free subsemigroups in the group of linear transformations of number fields. Bukovinian Mathematical Journal. 2018, 1
AMA Style: Sumaryuk MI. Free subsemigroups in the group of linear transformations of number fields. Bukovinian Mathematical Journal. 2018; 1(454).
Chicago/Turabian Style: Mykhailo Illich Sumaryuk. 2018. "Free subsemigroups in the group of linear transformations of number fields". Bukovinian Mathematical Journal. 1 no. 454.

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