On Schur 2-Groups

M. E. Muzychuk, I. N. Ponomarenko

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

A finite group G is called a Schur group if every Schur ring over G is the transitivity module of a point stabilizer in a subgroup of Sym(G) that contains all permutations induced by the right multiplications in G. It is proved that the group ℤ2×ℤ2n is Schur, which completes the classification of Abelian Schur 2-groups. It is also proved that any non-Abelian Schur 2-group of order larger than 32 is dihedral (the Schur 2-groups of smaller orders are known). Finally, the Schur rings over a dihedral 2-group G are studied. It turns out that among such rings of rank at most 5, the only obstacle for G to be a Schur group is a hypothetical ring of rank 5 associated with a divisible difference set.

Original languageEnglish
Pages (from-to)565-594
Number of pages30
JournalJournal of Mathematical Sciences
Volume219
Issue number4
DOIs
StatePublished - 1 Dec 2016
Externally publishedYes

ASJC Scopus subject areas

  • Statistics and Probability
  • Mathematics (all)
  • Applied Mathematics

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