Designed for mathematics majors who have completed calculus and linear algebra, this book introduces the fundamentals of mathematical proofs. It equips students with the necessary skills to analyze and construct proofs, emphasizing the axiomatic nature of mathematics. The content prepares them for the challenges of upper-level courses, ensuring a solid foundation in rigorous mathematical reasoning.
Starting with the Schur-Zassenhaus theorem, this monograph documents a wide variety of results concerning complementation of normal subgroups in finite groups. The contents cover a wide range of material from reduction theorems and subgroups in the derived and lower nilpotent series to abelian normal subgroups and formations. Contents Prerequisites The Schur-Zassenhaus theorem: A bit of history and motivation Abelian and minimal normal subgroups Reduction theorems Subgroups in the chief series, derived series, and lower nilpotent series Normal subgroups with abelian sylow subgroups The formation generation Groups with specific classes of subgroups complemented