BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//UNIFR/WEBMASTER//NONSGML v1.0//EN
CALSCALE:GREGORIAN
BEGIN:VEVENT
DTSTART;VALUE=DATE:20110524T171500
DTEND;VALUE=DATE:20110524T171500
UID:5633@agenda.unifr.ch
DESCRIPTION:Each group considered will have a finite number of elements. A  \ngroup is solvable if there exists a sequence of subgroups such that  \nfor each consecutive pair, the first one is a normal subgroup of the  \nsecond one, and the order (number of elements) of the second one is a  \nprime number times the order of the first one. For example, the group  \nof permutations of a set with 4 elements is of order 4! = 24, and it  \nis solvable because it possesses a sequence of subgroups with each  \nnormal in the next whose orders are 1, 2, 4, 12, and 24. We say H is  \na  Sylow p-subgroup of G if p is a prime and the order of H is the  \nhighest power of p that divides the order of G.  In the 1870's, Sylow  \nproved that each finite group has a Sylow p-subgroup for each prime p  \nand that furthermore, all the Sylow p-subgroups of G are conjugate,  \nand any conjugate of a Sylow p-subgroup is a Sylow p-subgroup.\n<br />\n<br />\n     The concept of injector is one of several generalizations of the  \nSylow subgroups. If F is a particular type of set of subgroups of a  \nsolvable group G called a Fitting set of G, then F contains a  \ncollection of subgroups which are maximal in a nice way. These  \nsubgroups are called the F-injectors of G, and they satisfy the  \nconditions above mentioned for Sylow p-subgroups: for each Fitting set  \nF of a solvable group G, there exists a conjugacy class of subgroups  \nconsisting of all the F-injectors of G.  The Sylow p-subgroups of G  \nare the F-injectors of G  when F is the Fitting set of p-subgroups of  \nG, i.e, the subgroups whose orders are powers of the prime p.\n<br />\n<br />\n      For the last several years, I have been working with Rex Dark  \nof the National University of Ireland, Galway, and Maria Dolores Perez- \nRamos of the University of Valencia, Spain to characterize the set of  \ninjectors of a finite solvable group G without reference to Fitting  \nsets. Thus we have been discovering properties of a subgroup H that  \nare necessary  and sufficient for the existence of some Fitting set F  \nfor which H is an F-injector. In this talk, I will define Fitting sets  \nand injectors, relate those concepts to Sylow subgroups, and mention  \nsome of our results.\n<br />\n<br />\nLaura Ciobanu
SUMMARY:Prof. Dr. Arnold D. FELDMAN (Lancaster / z.Zt. Galway): Solvable groups, Sylow subgroups and injectors
CATEGORIES:Colloque / Congrès / Forum
LOCATION:PER 08\, Phys 2.52\, Chemin du Musée 3\, 1700 Fribourg
URL;VALUE=URI:https://agenda.unifr.ch/e/fr/5633
END:VEVENT
END:VCALENDAR