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SUMMARY:Tony Bak (Bielefeld)
DTSTART:20201029T100000Z
DTEND:20201029T110000Z
DTSTAMP:20260419T060510Z
UID:CRMDS/25
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CRMDS/25/">S
 olution to the sandwich classification problem in arbitrary groups and app
 lications to classical-like groups over arbitrary rings</a>\nby Tony Bak (
 Bielefeld) as part of Western Sydney University Abend Seminars\n\n\nAbstra
 ct\nLet G be an arbitrary group and F an arbitrary subgroup. For each mixe
 d commutator subgroup K = [F\, H] of G\, we define the notion of an F-coco
 mmutator subgroup over K. The set of F-cocommutator subgroups over K forms
  a sandwich of subgroups of G\, which is denoted by Sand(K).  It has  a la
 rgest member C(K) called the full cocommutator subgroup over K and if F is
  perfect then K is its smallest member. C(K) is the replacement in the set
 ting of arbitrary groups for the notion of full congruence subgroup in the
  setting of classical-like groups over rings when F is the elementary subg
 roup and the K's are replacements for the relative elementary subgroups of
   a classical-like group. The MAIN THEOREM is:  A subgroup H of G is F-nor
 mal if and only if it belongs to a sandwich Sand(K) for some K.  Moreover 
 K is unique. We show that the known classification of E-normal subgroups o
 f a classical-like group G(R) over a quasi-finite ring R\, where E is the 
 elementary subgroup of G(R)\,  is a consequence of the Main Theorem and  w
 e use the Main Theorem to extend this result to classical-like groups G(R)
  over an arbitrary ring R.\n
LOCATION:https://researchseminars.org/talk/CRMDS/25/
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