Author
Zvonimir Janko
Bio: Zvonimir Janko is an academic researcher from Heidelberg University. The author has contributed to research in topics: Locally finite group & Abelian group. The author has an hindex of 7, co-authored 37 publications receiving 459 citations.
Papers
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Book•
01 Jan 2015
TL;DR: The fifth volume of a comprehensive and elementary treatment of finite p-group theory is as discussed by the authors, which includes many dozens of original exercises (with difficult exercises being solved) and a list of about 900 research problems and themes.
Abstract: 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.
254 citations
Journal Article•
TL;DR: 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; and 3) Classification of minimal nonmetacyclic p-group, classification of groups of odd order without normal elementary abelians of order p (power 3); and 4) Proofs of some basic counting theorems based on the new enumeration principle as discussed by the authors.
Abstract: 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.
46 citations
14 citations
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Book•
20 Nov 2014
TL;DR: This paper presents a meta-anatomy of the determinants of infectious disease in eight operation rooms of the immune system and some of the mechanisms involved are described.
Abstract: Zusammenfassung.- Introduction.- Fundamentals.- General results and methods.- Applications.- Bibliopraphy.- Index.- List of tables.
87 citations
TL;DR: In this article, the finite p -groups all of whose non-abelian proper subgroups are generated by two elements are classified and a classification of finite p-groups with two elements is given.
64 citations
TL;DR: In this paper, Niroom and Niroom et al. classify all capable nilpotent Lie algebras of finite dimension possessing a derived subalgebra of dimension one.
60 citations
TL;DR: In this paper, the authors derived 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 by means of relations for generators.
Abstract: 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.
44 citations