Michio Suzuki's monograph "Structure of a Group and the Structure of Its Lattice of Subgroups" discusses the relationship between a group and the lattice of its subgroups.
My question is: Is there a new monograph like Michio's or books presenting and discussing the new results?
Any references will be welcomed.
You might want to examine
Roland Schmidt
Subgroup lattices of groups.
De Gruyter Expositions in Mathematics. 14.
Berlin: Walter de Gruyter. xv, 572 p. (1994).
It's not a 'new' book, but it is much newer than Suzuki's 1956 book.
Here is the last sentence of the zbMATH review of Schmidt's book (review written by Hermann Heineken):
In the opinion of the reviewer the book is very well written – to wait for a new book in this area almost 40 years has proved to be worthwhile.
Here is a link to Ralph Freese's review of the book. This review appeared in the Bulletin of the American Mathematical Society in 1996.
Also this question is relevant (and in that answer, Keith Kearnes also refers to the same book he is referring here to).
I second the recommendation of Schmidt's book. I'll add that material from the point of view of order complexes (the simplicial complex of chains in a poset) is in Stephen Smith's Subgroup Complexes book. There are some pretty theorems here -- for example, you can tell by the topology of the order complex of a finite subgroup lattice whether your group was solvable or not.
