Tag Archives: semigroups

A permutation group challenge, 2

Posted on 26/12/2012 by

The result in the preceding post can be formulated as follows: A permutation group of degree n = 2k which is transitive on partitions of shape (k,k) but not on ordered partitions of this shape, has a fixed point and is (k−1)-homogeneous … Continue reading →

Posted in open problems | Tagged , , | 1 Comment

A permutation group challenge

Posted on 19/12/2012 by

Long ago, in the distant past before the Classification of Finite Simple Groups, Peter Neumann, Jan Saxl and I investigated the class of permutation groups acting on sets of even cardinality n = 2k, with the following interchange property: Any subset of … Continue reading →

Posted in exposition, open problems | Tagged , , , | 1 Comment

Semigroups, quasigroups

Posted on 31/07/2011 by

   Lisbon and Prague are two of the most beautiful cities in Europe. In the last week of July 2011, Lisbon hosted a conference on groups and semigroups, and Prague one on quasigroups and loops. I was at the Lisbon … Continue reading →

Posted in events, exposition | Tagged , , , , | 8 Comments

Transitivity and synchronization

Posted on 15/07/2011 by

Let Sn be the symmetric group of all permutations of {1,…,n}, and Tn the full transformation monoid of all functions from this set to itself. Recently I have come to the meta-conjecture that there is a fairly close analogy between … Continue reading →

Posted in exposition, open problems | Tagged , , , , , , | Leave a comment