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SUMMARY:Mima Stanojkovski (Max-Planck-Institut Leipzig)
DTSTART:20210121T160000Z
DTEND:20210121T170000Z
DTSTAMP:20260423T021328Z
UID:GOThIC/14
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GOThIC/14/">
 On the modular isomorphism problem for groups of class $3$</a>\nby Mima St
 anojkovski (Max-Planck-Institut Leipzig) as part of GOThIC - Ischia Online
  Group Theory Conference\n\n\nAbstract\nLet $G$ be a finite group and let 
 $R$ be a commutative ring. In 1940\, G.\nHigman asked whether the isomorph
 ism type of $G$ is determined by its\ngroup ring $RG$. Although the Isomor
 phism Problem has generally a negative\nanswer\, the Modular Isomorphism P
 roblem (MIP)\, for $G$ a $p$-group and $R$ a\nfield of positive characteri
 stic $p$\, is still open. Examples of $p$-groups\nfor which the (MIP) has 
 a positive solution are abelian groups\, groups\nof order dividing $2^9$ o
 r $3^7$ or $p^5$\, certain groups of maximal class\,\netc.\n\nI will give 
 an overview of the history of the (MIP) and will present\nrecent joint wor
 k with Leo Margolis for groups of nilpotency class $3$. In\nparticular\, o
 ur results yield new families of groups of order $p^6$ and\n$p^7$ for whic
 h the (MIP) has a positive solution and a new invariant for certain\n$2$-g
 enerated groups of class $3$.\n
LOCATION:https://researchseminars.org/talk/GOThIC/14/
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