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SUMMARY:Alan Camina
DTSTART:20251104T140000Z
DTEND:20251104T150000Z
DTSTAMP:20260421T153940Z
UID:UEAPS/61
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/UEAPS/61/">C
 osets of normal subgroups: what can they tell us about the group</a>\nby A
 lan Camina as part of ANTLR seminar\n\nLecture held in C. HALL 01.08.\n\nA
 bstract\nIn this talk we discuss how information about the non-trivial cos
 ets of a normal subgroup  can influence the structure of a finite group.\n
 \nHere is one example:\n\nLet $G$ be a finite group with a normal subgroup
  $N$. Assume that for each non-trivial coset $Nr$ all the elements in $Nr$
  have the same order.\n\nThen one of the following holds:\n\n1.  $N < F(G)
 $\, in this case $F(G)$\, and hence $N$\, is a $p$-group for some prime $p
 $.\n\n2.  $N = F(G)$.\n\n3.  $F(G) < N$ in this case $G/N$ is a $p$-group.
 \n\nHere $F(G)$ is the Fitting subgroup of $G$.\n
LOCATION:https://researchseminars.org/talk/UEAPS/61/
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