Charlotte Scott Centre for Algebra

School of Mathematics & Physics, University of Lincoln

New paper in a high-ranking journal

Congratulations to Dr Simon Smith on his paper being published in Duke Mathematical Journal, one of the most prestigious and highest-ranking journals in mathematics!

In this paper, “A Product for Permutation Groups and Topological Groups“, Simon introduces a new product for permutation groups, called the box product. It takes as input two permutation groups, M and N, and produces an infinite group which carries many of the permutational properties of M. Surprisingly, the box product preserves primitivity under the same conditions as the wreath product acting in its product action.

When M and N are thought of as topological groups, the product provides a general way to build exotic examples of groups in the class S of non-discrete, topologically simple, totally disconnected, locally compact, compactly generated topological groups. Simon uses the box product to obtain the first construction of uncountably many pairwise non-isomorphic groups in S.

Simon’s results not only answer important questions about the structure of groups in the class S, but open new areas of research in group theory based on his new operation on groups, the box product.

2 comments on “New paper in a high-ranking journal

  1. Evgeny Khukhro
    February 14, 2018

    Reblogged this on Maths & Physics News.

    Like

  2. Pingback: Simon Smith’s talk at the British Mathematical Colloquium 2018 | Charlotte Scott Centre for Algebra

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google+ photo

You are commenting using your Google+ account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s

This site uses Akismet to reduce spam. Learn how your comment data is processed.

Information

This entry was posted on February 14, 2018 by in New publications, research.
%d bloggers like this: