Maria Kolinko

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math.GR2023

Midconvex sets in Abelian groups

Iryna Banakh, Taras Banakh, Maria Kolinko +1

A subset $X$ of an Abelian group $G$ is called $mi d co n v e x$ if for every $x, y \in X$ the set $\frac{x + y}{2} = {z \in G : 2 z = x + y}$ is a subset of $X$ . We prove that a subset $X$ of an Abel…

math.GR2023

Semiaffine sets in Abelian groups

Iryna Banakh, Taras Banakh, Maria Kolinko +1

A subset $X$ of an Abelian group $G$ is called $se mia f f in e$ if for every $x, y, z \in X$ the set ${x + y - z, x - y + z}$ intersects $X$ . We prove that a subset $X$ of an Abelian group $G$ …