2. Professors
  3. MONETTA Carmine
  4. Teaching

GRUPPI LOCALMENTE FINITI

Carmine MONETTA GRUPPI LOCALMENTE FINITI

8860300011
DIPARTIMENTO DI MATEMATICA
Corso di Dottorato (D.M.226/2021)
MATHEMATICS
2022/2023

YEAR OF COURSE 1
YEAR OF DIDACTIC SYSTEM 2022
FULL ACADEMIC YEAR
CFUHOURSACTIVITY
210LESSONS
CARMINE MONETTA T Curriculum
Objectives
THE AIM OF THIS COURSE IS TO INVESTIGATE SOME CLASSES OF INFINITE GROUPS.

RECENT WORKS ON THE TOPIC WILL BE ANALYZED. MOREOVER, WE WILL PRESENT SOME TOOLS TO CONSTRUCT NEW EXAMPLES OF GROUPS, AS WELL AS, TO RECOGNIZE THE MAIN PROPERTIES OF A LOCALLY FINITE GROUP.
Prerequisites
BASIC KNOWLEDGE OF GROUP THEORY, AS SYLOW'S THEOREMS.
Contents
PASSING FROM THE STUDY OF FINITE GROUPS TO THAT OF GROUPS OF ANY CARDINALITY, QUITE NATURALLY ONE ENCOUNTERS THE CLASS OF LOCALLY FINITE GROUPS, THAT IS, THE CLASS OF GROUPS IN WHICH EVERY FINITELY GENERATED SUBGROUP IS FINITE. IT IS CLEAR THAT LOCAL FINITENESS IS A FINITENESS CONDITION, THAT IS, A PROPERTY POSSESSED BY EACH FINITE GROUP, AND IT IS PERHAPS THE CLOSEST TO FINITENESS AMONG ALL.

THE OBJECTIVE OF THIS COURSE INDEED IS TO ILLUSTRATE THE MAIN PROPERTIES OF LOCALLY FINITE GROUPS, SHOWING THAT MANY VALID THEOREMS FOR FINITE GROUPS NOT ONLY CAN BE SUITABLY MODIFIED TO MAKE SENSE FOR THE CLASS OF LOCALLY FINITE GROUPS, BUT THAT THEY OFTEN CONTINUE TO BE VALID FOR SUCH GROUPS.
Teaching Methods
LECTURES AND TEAM EXERCISES.
Verification of learning
A SHORT SEMINAR ON A TOPIC NOT DEVELOPED DURING THE LECTURES.
Texts
ASAR, A.O., THE SOLUTION OF A PROBLEM OF KEGEL AND WEHRFRITZ, PROC. LONDON MATH.
SOC. (3) 45 (1982), 337-364.

DIXON, M.R., SYLOW THEORY, FORMATIONS AND FITTING CLASSES IN LOCALLY FINITE GROUPS,
WORLD SCIENTIFIC, SINGAPORE 1994.

D. J. S. ROBINSON, A COURSE IN THE THEORY OF GROUPS, 2ND EDITION, SPRINGER-
VERLAG, NEW YORK, 1996.
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