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SUMMARY:Anastasia Hadjievangelou (University of Bath)
DTSTART:20230130T140000Z
DTEND:20230130T150000Z
DTSTAMP:20260423T021330Z
UID:GANT/19
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GANT/19/">Le
 ft 3-Engel Elements in Locally Finite p-groups</a>\nby Anastasia Hadjievan
 gelou (University of Bath) as part of Greek Algebra & Number Theory Semina
 r\n\n\nAbstract\nEngel Theory is of significant interest in group theory a
 s there\nis an unmistakable correlation between Engel and Burnside problem
 s. In\nthis talk we first introduce Engel elements and Engel groups and in
 \nparticular we expand our knowledge on locally finite Engel groups. It is
 \nimportant to know that M. Newell proved that if $x$ is a right $3$-Engel
 \nelement in a group $G$ then $x$ lies in $HP(G)$ (Hirsch-Plotkin radical)
  and in\nfact he proved the stronger result that the normal closure of $x$
  is\nnilpotent of class at most $3$. The natural question arises whether t
 he\nanalogous result holds for left $3$-Engel elements. We will give vario
 us\nexamples of locally finite p-groups $G$ containing a left $3$-Engel el
 ement $x$\nwhose normal closure is not nilpotent. Lastly\, we will discuss
  the open\nproblem of whether or not a left $3$-Engel element always lies 
 in the $HP(G)$.\n(This is joint work with Gunnar Traustason and Marialaura
  Noce)\n
LOCATION:https://researchseminars.org/talk/GANT/19/
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