An answer to Hirasaka and Muzychuk : every p - Schur ring over C 3 p is Schurian Dedicated to the memory of Jiping ( Jim )
نویسندگان
چکیده
In [HiMu] the authors, in their analysis on Schur rings, pointed out that it is not known whether there exists a non-Schurian p-Schur ring over an elementary abelian p-group of rank 3. In this paper we prove that every p-Schur ring over an elementary abelian p-group of rank 3 is in fact Schurian.
منابع مشابه
COMMUTATIVE p-SCHUR RINGS OVER NON-ABELIAN GROUPS OF ORDER p
Recently, it was proved that every p-Schur ring over an abelian group of order p is Schurian. In this paper, we prove that every commutative p-Schur ring over a non-abelian group of order p is Schurian.
متن کاملAbelian p - groups of rank greater than or equal to 4 p − 2 are not CI - groups
In this paper we prove that an elementary Abelian p-group of rank 4p− 2 is not a CI(2)-group, i.e. there exists a 2-closed transitive permutation group containing two non-conjugate regular elementary Abelian p-subgroups of rank 4p − 2, see Hirasaka and Muzychuk (J. Comb. Theory Ser. A 94(2), 339–362, 2001). It was shown in Hirasaka and Muzychuk (loc cit) and Muzychuk (Discrete Math. 264(1–3), 1...
متن کاملAutomorphism Groups of Schur Rings
In 1993, Muzychuk [18] showed that the rational Schur rings over a cyclic group Zn are in one-to-one correspondence with sublattices of the divisor lattice of n, or equivalently, with sublattices of the lattice of subgroups of Zn. This can easily be extended to show that for any finite group G, sublattices of the lattice of characteristic subgroups of G give rise to rational Schur rings over G ...
متن کاملStrongly regular Cayley graphs over primary abelian groups of rank 2
Strongly regular Cayley graphs with Paley parameters over abelian groups of rank 2 were studied in [5] and [12]. It was shown that such graphs exist iff the corresponding group is isomorphic to Zpn ⊕Zpn , where p is an odd prime. In this paper we classify all strongly regular Cayley graphs over this group using Schur rings method. As a consequence we obtain a complete classification of strongly...
متن کاملCompleteness results for metrized rings and lattices
The Boolean ring $B$ of measurable subsets of the unit interval, modulo sets of measure zero, has proper radical ideals (for example, ${0})$ that are closed under the natural metric, but has no prime ideal closed under that metric; hence closed radical ideals are not, in general, intersections of closed prime ideals. Moreover, $B$ is known to be complete in its metric. Togethe...
متن کامل