The modular isomorphism problem for the groups of order 512. (English) Zbl 1231.20002

Campbell, C.M. (ed.) et al., Groups St. Andrews 2009. Vol. II. Selected papers of the conference, University of Bath, Bath, UK, August 1–15, 2009. Cambridge: Cambridge University Press (ISBN 978-0-521-27904-8/pbk). London Mathematical Society Lecture Note Series 388, 375-383 (2011).
Summary: For a prime \(p\) let \(G\) be a finite \(p\)-group and \(K\) a field of characteristic \(p\). The Modular Isomorphism Problem (MIP) asks whether the modular group algebra \(KG\) determines the isomorphism type of \(G\). We briefly survey the history of this problem and report on our computer-aided verification of the Modular Isomorphism Problem for the groups of order 512 and the field \(K\) with 2 elements.
For the entire collection see [Zbl 1219.20003].


20C05 Group rings of finite groups and their modules (group-theoretic aspects)
16S34 Group rings
20D15 Finite nilpotent groups, \(p\)-groups