Type: Article
Publication Date: 2022-07-25
Citations: 8
DOI: https://doi.org/10.1007/s10998-022-00483-5
Abstract Let G be a group and $$G_0 \subseteq G$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>G</mml:mi> <mml:mn>0</mml:mn> </mml:msub> <mml:mo>⊆</mml:mo> <mml:mi>G</mml:mi> </mml:mrow> </mml:math> be a subset. A sequence over $$G_0$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>G</mml:mi> <mml:mn>0</mml:mn> </mml:msub> </mml:math> means a finite sequence of terms from $$G_0$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>G</mml:mi> <mml:mn>0</mml:mn> </mml:msub> </mml:math> , where the order of elements is disregarded and the repetition of elements is allowed. A product-one sequence is a sequence whose elements can be ordered such that their product equals the identity element of the group. We study algebraic and arithmetic properties of monoids of product-one sequences over finite subsets of G and over the whole group G , with a special emphasis on the infinite dihedral group.