In 1931, we made an effort to find common divisors in order to cancel fractions, in the second year of secondary school in Wriezen - I wistfully remember this little old town in the East ... The excessive thoroughness of this procedure bored me, and coaxed me into declaring that one merely had to try up to the difference of the numerator from the denominator. The mathematics teacher, Mr Kempin, who had tolerated our efforts without this constraint, turned to the blackboard, perhaps a little embarrassed. There he probably wrote down this line, which confirmed my remark, but which I did not yet understand:

$a = ud, b = vd \Rightarrow a - b = (u - v)d$

The memory of my discovery of this beneficial little theorem from number theory then remained such a distinct one probably because it was a first mathematical experience for me, and because the praise I received for it afterwards encouraged me to perform well in mathematics from then on. Out of everything that I have accomplished so far this is proof to myself that I am a mathematician more than anything else.

In 1946, all of us students lived in the berths of the Orla, a ship ready to be handed over to the English. We lived on barter in all areas of life. Among my meek belongings was a rather special mathematics book. It had been published in 1942, and after the disastrous winter in the East the wartime economy must have deemed it beneficial to winning the war and therefore worthy of publication, despite the shortage in demand, due to its title: 'The Geometry of Fabrics'. In any case, to me it seemed dispensable as a basis for studying mathematics. - One of my roommates offered me a book for it, whose title admittedly meant less to me, but which would hardly hold less interest for me than mine. The exchange was made. The book that I had acquired then became a revelation to me: Andreas Speiser's 'Group Theory'. ... The effects that this simple exchange of books had on the development of the mathematical seminar in Kiel can arguably still be perceived today. This is an example that shows how minor variations of the initial conditions can influence the solutions of an equation considerably.

I could reject the chair at Karlsruhe on the grounds that, following ancient family tradition, Karl was one of my given names and that Karlshof - often written with 'ff' by its owners - was my place of birth. Being in my early forties, to me Karlsruhe clearly had to forebode all too early scientific twilight years. - In short, I stayed in Kiel, with the same offer and keeping the abundant range of research projects. The decision was much more difficult when I was appointed to Mainz, where my colleague Bertram Huppert was one of the main figures. I had been communicating with him on scientific matters for a long time, through the medium of Helmut Wielandt, our great mentor in group theory; and we were united by a fate: Huppert's book - no, not book, but thesaurus on finite groups. - The genesis of this plan of creating the book had committed me to participate in the editing process and to contribute my humble advice. ... Thus Huppert visited us in Kiel for four weeks per year, allegedly to use the assistance of me and other colleagues from Kiel. In reality this endeavour proved to be a marvellous and gratefully used opportunity for our seminar to thoroughly keep up with the latest developments. ... I had become so accustomed to this close and convenient collaboration with Huppert, that, with my propensity to be sedentary, I stayed in the seminar in Kiel, which I had grown fond of.

Let us formulate a problem on complements. Let $N$ be a normal subgroup of a group $G$. When does $G$ contain at least one complement $C$ to $N$, and when are two given complements $C, C_{1}$ to $N$ conjugate in $G$? The important contribution to studying this problem is due to Gaschütz.

A database search in 1990 brought to light some 38 articles having "prefrattini subgroup" either in their title or cited as a key phrase, which is convincing evidence that Gaschütz's original idea has been widely investigated and variously generalized.

After completion of the classification of simple groups the main problem in the theory of finite groups remains the problem of mastering mechanisms of their interaction in arbitrary groups. The most important handicap here is p-groups.

The theory of formations, as well as the theory of Fitting classes, is an attempt to be engaged in the theory of groups, that is to say, modulo p-groups. For all that, separate groups are considered through these classes as if in a diminishing glass, and structural operations on groups can be treated, in a definite respect, as construction of normalizers, extensions, joins, etc.