Zusammenfassung.- Introduction.- Fundamentals.- General results and methods.- Applications.- Bibliopraphy.- Index.- List of tables.

Blocks of Finite Groups and Their Invariants

Structure of a group and the structure of its lattice of subgroups

Finite p-groups all of whose non-abelian proper subgroups are generated by two elements

Some criteria for detecting capable Lie algebras

Explicit expressions for the transfers V i from a metabelian p-group G of coclass cc(G) = 1 to its maximal normal subgroups M 1, . . . , M p+1 are derived by means of relations for generators. The expressions for the exceptional case p = 2 differ significantly from the standard case of odd primes p ≥ 3. In both cases the transfer kernels Ker(V i ) are calculated and the principalisation type of the metabelian p-group is determined, if G is realised as the Galois group \({{\rm{Gal}}({F}_p^2(K)\vert K)}\) of the second Hilbert p-class field \({{F}_p^2(K)}\) of an algebraic number field K. For certain metabelian 3-groups G with abelianisation G/G′ of type (3, 3) and of coclass cc(G) = r ≥ 3, it is shown that the principalisation type determines the position of G on the coclass graph \({\mathcal{G}(3,r)}\) in the sense of Eick and Leedham-Green.

Transfers of metabelian p-groups

This is the fifth volume of a comprehensive and elementary treatment of finite p-group theory. Topics covered in this volume include theory of linear algebras and Lie algebras. The book contains many dozens of original exercises (with difficult exercises being solved) and a list of about 900 research problems and themes.

Groups of Prime Power Order 4

Groups of Prime Power Order, Volume 1

The following main results are proved: 1) Classification of p-groups all of whose subgroups of index p (square power)are abelian. 2) Classification of p-groups with 7 involutions. 3) New proofs of some Blackburn's results (classification of minimal nonmetacyclic p-groups, classification of p-groups of odd order without normal elementary abelian subgroup of order p (power 3)). 4) Proofs of some basic counting theorems based on the new enumeration principle. 5) New proof of Ward's theorem on quaternion-free 2-groups. 6) Corrected proof of Iwasawa's theorem on the structure of modular p-groups. Our proofs are completely elementary.

Structure of Finite p-groups with Given Subgroups

Groups of Prime Power Order, Volume 2

We give a complete classification of finite p-groups all of whose noncyclic subgroups are normal, which solves a problem stated by Berkovich.

/pdf/a-complete-classification-of-finite-p-groups-all-of-whose-4sds4rf6kj.pdf

Zvonimir Janko

Papers

Groups of Prime Power Order 4

Groups of Prime Power Order, Volume 1

Structure of Finite p-groups with Given Subgroups

Groups of Prime Power Order, Volume 2

A complete classification of finite p-groups all of whose noncyclic subgroups are normal