Reminder on Tadeusz Kantor

Professor Tadeusz Tumidajski

Tadeusz Marek Krygowski

Tadeusz Batóg's Phonological Systems

The phonological works of Tadeusz Batóg concern rst of all the logical reconstruction of the concept of the phoneme. It should be stressed at the very beginning that the works in question have established a standard which should be recommended in all attempts at a logical reconstruction of linguistic theories. The Author uses, along with the standard machinery of the classical predicate calculu...

Normality in a Kantor Family

A Kantor family is a collection of subgroups from which a generalized quadrangle can be constructed using Kantor ' s idea. This paper considers the case in which some of the subgroups in the Kantor family or its related family are normal in the ambient finite group G. We show that if two members of a Kantor family are normal in G then G is elementary abelian and that if all members of the relat...

Finite Groups that Admit Kantor Families

The basic problem of interest in this note is: What finite groups G admit a Kantor family (i.e., 4-gonal family) of subgroups? We begin with a survey of the known examples (of the groups G, not of the Kantor families) and then pose the question of whether or not two specific examples are isomorphic. The two groups in question have order q and coexist for q = 3 ≥ 27. Our conjecture had been that...