The book "Recognition of alternating groups of simple degree by the order of their elements" by the authors Kondratiev A. C. and Mazurova V. D. is a unique study in algebra and group theory that will be of interest to both students and professional mathematicians. This publication is not just a textbook, but a real guide to the complex concepts that underlie modern abstract algebra. The book focuses on the topic of alternating groups that play a key role in various areas of mathematics and its applications. The authors offer readers a deep dive into group theory, exploring their structures and properties through the prism of the order of the elements. This allows not only to understand how groups function, but also to develop the analytical thinking needed to solve complex problems. The book will be especially useful for senior students of mathematical faculties, graduate students and teachers, as well as for anyone interested in algebra and its applications. If you are passionate about mathematics and want to expand your knowledge of groups, then this publication will become a real storehouse of information for you. In it you will find both theoretical foundations and practical examples that will help to consolidate the knowledge gained. The topics raised in the book cover a wide range of issues, including the classification of variable groups, how to recognize them, and the analysis of their properties. The authors emphasize the importance of understanding the structure of groups for solving more complex mathematical problems. They offer readers not only theoretical calculations, but also practical tasks that will help to consolidate the material and develop analytical skills. The style of the authors is distinguished by clarity and accessibility of presentation, which makes complex mathematical concepts more understandable. Kondratiev A. C. and Mazurov V. D. are known for their scientific work in the field of algebra, and their authority in this area gives the book additional value They skillfully combine theory with practice, which allows readers not only to assimilate the material, but also to apply it to real-world problems. This book will be an excellent addition to the library of any mathematician, and will also be useful for those interested in theoretical physics, computer science and other disciplines where group theory finds its application. If you are looking for literature that will help you understand complex mathematical concepts and expand your horizons, then “Recognizing simple degree variable groups by the orders of their elements” is exactly what you need. Do not miss the opportunity to immerse yourself in the world of abstract algebra with this fascinating and informative edition. The book will be your reliable companion in the study of group theory and will help you open new horizons in mathematics.