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SUMMARY:Michael Vaughan-Lee (Christ Church\, Oxford)
DTSTART:20211104T170000Z
DTEND:20211104T180000Z
DTSTAMP:20260423T053138Z
UID:GOThIC/43
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GOThIC/43/">
 Schur’s exponent conjecture</a>\nby Michael Vaughan-Lee (Christ Church\,
  Oxford) as part of GOThIC - Ischia Online Group Theory Conference\n\n\nAb
 stract\nIf $G$ is a finite group and we write $G = F/R$ where $F$ is a fre
 e group\,\nthen the Schur multiplier $M(G)$ is $(R \\cap F')/[F\, R]$.\n\n
 There is a long-standing conjecture attributed to I. Schur that the expone
 nt of $M(G)$ divides the exponent of $G$. It is easy to show that this is 
 true\nfor groups $G$ of exponent $2$ or exponent $3$\, but it has been kno
 wn since 1974\nthat the conjecture fails for exponent $4$. However the tru
 th or otherwise of\nthis conjecture has remained open up till now for grou
 ps of odd exponent.\n\nIn my talk I describe counterexamples to the conjec
 ture of exponent $5$\nand exponent $9$.\n\nI also give some suggestions fo
 r further counterexamples\, and explore the\npossibilities for alternative
  conjectures.\n
LOCATION:https://researchseminars.org/talk/GOThIC/43/
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