The Lyapin's notebook: a collection of unsolved problems in Semigroup Theory

TL;DR

This paper compiles significant unsolved problems in semigroup theory, highlighting key research directions and serving as a guide for future investigations in algebraic systems.

Contribution

It presents a curated collection of open problems in semigroup theory, honoring E. S. Lyapin and outlining contemporary research challenges.

Findings

Identifies major open problems in semigroup potential properties and embeddability.

Highlights unresolved issues in structural and finiteness conditions in varieties.

Provides a roadmap for future research in algebraic systems.

Abstract

This collection presents a selected set of unsolved problems in semigroup theory, a fundamental branch of modern algebra. The publication is dedicated to the 110th anniversary of the birth of E. S. Lyapin, one of the founders of the field and the author of the world's first monograph on semigroups. The collection covers several major directions of contemporary research: potential properties and embeddability of semigroups; structural problems and finiteness conditions in varieties; endomorphisms; solvable and unsolvable classes of finite semigroups and groups; power semigroups; inclusive varieties; and the theory of partial groupoids. It serves both as a tribute to Lyapin's memory and as a roadmap for current and future research in algebraic systems.