Anyone familiar with Fraleigh's A First Course in Abstract Algebra 7th ed? I'm using it in my self-study of algebra. The first three chapters (Groups and Subgroups, Permutations-Cosets-Direct Products, Homomorphisms and Factor Groups) tackle about group theory. Chapter 4 is "Rings and Field", Chapter 5 "Ideals and Factor Rings", and Chapter 6 "Extension Fields".
I already finished the first 3 chapters, but I don't want to proceed with rings yet. Can I jump into Chapter 7 which is "Advanced Group Theory" and to Chapter 8 "Groups in Topology" (I only finished Chapter 1 and 2 of Munkres' Topology)?
Or is there an advantage of studying the basics of rings first before delving into more advanced topics of group theory?
The table of dependencies (p. xiii) indicates that Chapter VII (Sections 34-40) depends only on Sections 1-16 (Chapters I-III) (and only Sections 36-37 use Section 16, and nothing depends on Section 17). Chapter VIII (Sections 41-44) depends only on Sections 1-15 and 38.
Why put this material so deep into the book? Some (but not all) math departments want to include some ring theory in their first semester abstract algebra course, so that a student who takes only one course will leave with some exposure to rings.