In memoriam Zvonimir Janko

 Zvonimir Janko (1932-2022) 




With a deep sense of loss we would like to communicate that the world famous Croatian mathematician Zvonimir Janko passed away on April 12, 2022. He made a great impact to finite group theory and combinatorial design theory. Professor Janko was not only an expert but a nice and generous person as well, always willing to help. As such he will be overwhelmingly missed by his former students, colleagues, friends and family. 

Zvonimir Janko was born on July 26, 1932, in Bjelovar, Croatia. He studied mathematics at the University of Zagreb, Croatia. After graduation he taught physics at a high school in Siroki Brijeg in Bosnia and Herzegovina, ˇ where he met his future wife Zora. He earned his PhD at the University of Zagreb in 1960. In his thesis, entitled Decomposition of some classes of nondegenerate R´edei Groups on Schreier extensions, Zvonimir Janko solved a problem posed by the Hungarian mathematician L´aszl´o R´edei. 

Janko spent two years at The Australian National University in Canberra (1962-1964), where he found his first sporadic simple group, now known as J1. This surprising discovery of the sporadic group J1, the first sporadic group found in the 20th century after the 19th century discovery of the five sporadic simple groups by Emile L´eonard Mathieu, brought Janko ´ the position of full professor at the Monash University in Melbourne, in 1965 at the age of 33. Zvonimir Janko worked at the Monash University from 1965 to 1968, whereas from 1968 to 1969 he was a visiting professor at the Princeton University, and then became a full professor at the Ohio State University in Columbus. Since 1972 Janko was a full professor at the University of Heidelberg, until his retirement in 2000. Even after his retirement, professor Janko had been very active and published many research papers and books. 

Zvonimir Janko’s work can be divided into three parts: finite simple groups (in the 1960s and the 1970s), combinatorial designs (in the 1980s and the 1990s), and p-groups (after 2000). Although he obtained significant results in all of these three research areas, his most important and most influential results are the discoveries of four sporadic finite simple groups, known as the Janko groups and denoted by J1, J2, J3 and J4. Especially, Janko’s discovery of the first Janko group J1, the first sporadic finite simple group discovered in the 20th century, was a breakthrough in group theory that motivated the search for other sporadic finite simple groups. Janko’s discovery of the group J1, together with his discovery of the sporadic finite simple groups J2, J3 and J4, made a great impact to the classification of finite simple groups, which is the most important result in theory of finite groups and one of the most important results in mathematics in general. Professor Janko delivered an invited lecture about his results on sporadic groups at the International Congress of Mathematicians in Nice, France, in 1970. 

Switching to design theory, Zvonimir Janko was mostly interested in proving the existence of certain combinatorial structures. He proved, sometimes in collaboration with Tran van Trung, the existence of symmetric designs with parameters (70,24,8), (71,21,6), (78,22,6), (189,48,12) and (105,40,15). Further, together with Vladimir Tonchev he proved the existence of a (nonsymmetric) 2-(175,7,1) design. Moreover, together with Hadi Kharaghani and Vladimir Tonchev he proved the existence of Bush-type Hadamard matrices of order 36, 100 and 324, which lead to construction of infinite series of symmetric designs and strongly regular graphs. Willing to be confronted 51 to the greatest problems in mathematics, Zvonimir Janko investigated the possibility of the existence of a projective plane of composite order as well. 

Zvonimir Janko was working in design theory for about 20 years when he returned to his first love, that is, group theory. In the 2000s, he started to study groups of prime power order. His work on p-groups and collaboration with Yakov Berkovich resulted in a large number of papers together with volumes 2 to 6 of the monograph series Groups of prime power order. Janko was always willing to work with students and share research problems with them. According to the Mathematical Genealogy Project, Zvonimir Janko had 18 PhD students and 87 descendants. He was a corresponding member of the Croatian Academy of Sciences and Arts, and a member of the Heidelberg Academy of Sciences. In 1970 the French Academy of Sciences decorated him with a medal for the discovery of sporadic groups. 

Zvonimir Janko was deeply devoted to his wife Zora, who sadly passed away in 2019. They are survived by their two children, Boris and Antoinette. 

Dean Crnkovi´c Faculty of Mathematics University of Rijeka Radmile Matejˇci´c 2, 51000 Rijeka, Croatia 

Mario Osvin Pavˇcevi´c Department of Applied Mathematics Faculty of Electrical Engineering and Computing University of Zagreb Unska 3, 10000 Zagreb, Croatia 52

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