It is a classical problem of algebraic number theory to decide if a number field is monogene and to determine all generators of its power integral bases. The problem can be reduced to the resolution of a certain type of diophantine e quations called index form equations.

In some cases these index fo rm equations are Thue equations or can be solved by using Thue equations (a nd its generalizations). Therefore we explain the basic methods of solving one of the most classical types of diophantine equations, the Thue equation s.

Some recent results are on infinite parametric families of numb er fields and on the problem of monogenity and power integral bases in thes e families of fields. DTSTAMP:20191214T231702Z DTSTART;TZID=Europe/Budapest:20180418T100000 DTEND;TZID=Europe/Budapest:20180418T120000 SEQUENCE:0 TRANSP:OPAQUE END:VEVENT END:VCALENDAR