Faculty of Mathematics, University of Rijeka, 51000 Rijeka, Croatia
e-mail:deanc@math.uniri.hr
Department of applied mathematics, Faculty of Electrical Engineering and Computing, University of Zagreb, 10000 Zagreb, Croatia
e-mail:mario.pavcevic@fer.hr
This special issue of Glasnik Matematički memorializes and honors Zvonimir Janko (1932-2022). The issue is a recognition of his far-reaching contributions and influence in the areas of finite group theory and combinatorial design theory. The issue contains 12 papers written by Zvonimir Janko's colleagues and students, to whom we proudly belong. These papers reflect Janko's interests, impact and proficiency in different areas of algebra and discrete mathematics.
On April 12, 2022, Zvonimir Janko passed away at his home in Heidelberg, Germany. He was buried in a cemetery in Heidelberg close to his home, together with his beloved wife Zora, who passed away in 2019.
Zvonimir Janko was born on July 26, 1932 in Bjelovar, Croatia. Although he lived most of his life outside Croatia, he visited Croatia every year and his unconditional love for Croatia was widely known. He completed his studies in mathematics in 1956 at the University of Zagreb and received his doctorate in mathematics in 1960 at the same university. At the beginning of 1962, he went to Australia, first to the Australian National University in Canberra, where he stayed until 1964, after which he got a professorship at Monash University in Melbourne, where he stayed until 1968, with a one-semester study stay at the University of Bonn. From 1968 to 1969, he was a visiting professor at Princeton University, from where he moved as a professor to the Ohio State University in Columbus, where he remained until 1972. That year, he returned to Europe and received a prestigious professorship at the Mathematical Institute of the University of Heidelberg, where he was employed until his retirement in 2000. As an emeritus professor, he remained active both as a scientist and an advisor until his very late days.
Zvonimir Janko gained world fame and recognition by finding four sporadic finite simple groups, which were named Janko groups after him and are usually denoted by \(J_1\), \(J_2\), \(J_3\) and \(J_4\). The discovery of the first of these groups in 1964 caused great surprise, even a shock between group theorists, since Mathieu groups, discovered in the 19th century, were thought to be the only sporadic finite simple groups. Janko's discovery of the group \(J_1\) played a decisive role in the classification of finite simple groups.
Janko's research can be divided into three parts. In the 1960s and 1970s, he dealt with finite simple groups, in the 1980s and 1990s with combinatorial designs, and after 2000 he devoted himself to the theory of \(p\)-groups. While Professor Janko's work in theory of finite groups was devoted to the classification of finite simple groups, his work in combinatorial design theory was mainly motivated by proving the existence of symmetric designs with certain parameters. In his work on \(p\)-groups, together with Yakov Berkovich, he published a six volumes monograph Groups of prime power order, a comprehensive work with a vast number of recent results and open problems.
Zvonimir Janko published around 130 research papers. He was a fruitful supervisor as well, supervising 18 PhD students. Professor Janko was a brilliant and insightful mathematician, a conscientious unpretentious advisor, a favorite teacher with a distinguished sense of humor and a warm family man. He is survived by his two children, Antoinette and Boris. Zvonimir Janko will be dearly missed by all of us who were influenced by his mathematical genius and human kindness.