Analogs of the lower and upper central series in skew braces

Abstract: Skew brace is a ring-like and group-like algebraic structure that was introduced in the study of set-theoretic solutions to the Yang-Baxter equation. In this paper, we shall give a survey on the left series, right series, socle series, and annihilator series of skew braces. They are analogs of the lower and upper central series of groups. Other than the well-known facts regarding these series, we shall also prove several new results about the relationship among their terms.