Skip to main content

Dr. Barnea Publishes in Top Journal

Dr. Barnea Publishes in Top Journal

  • Date26 June 2020

Dr. Barnea and Prof. Schlage-Puchta (University of Rostock, Germany) solve a well-known open problem in Group Theory.

Dr Barnea and Prof Schlage-Puchta

A result of seven years of collaboration between Dr. Barnea and Prof. Schlage-Puchta has led to a publication in one of the most prestigious mathematics journals "Forum of Mathematics, Pi".

In the paper, the authors solve a well-known open problem in the field of Group Theory. A group is an abstract algebraic way to describe symmetries. In essence, Dr. Barnea and Prof. Schlage-Puchta show that some type of groups (pro-p groups) can have almost any possible ‘size’ (subgroup growth).

A pro-p group is a type of group which can be constructed from a particular type of finite groups (finite p-groups, these are groups of size a power of a prime). A subgroup is a group that is a subset of a larger group. It's index is a number that measures in some sense how close it is to the larger group. Given a group G, let s(n) be the number of subgroups of G of index n. Subgroup growth is the asymptotic behaviour of the sequence (s(n)) when n goes to infinity. A fast subgroup growth means the group is in some sense ‘large’, while a slow subgroup growth means it is ‘small’.

Dr. Barnea and Prof. Schlage-Puchta proved that almost any subgroup growth can be achieved for pro-p groups. This natural problem was formulated by Lubotzky and Segal in their 2003 award winning book ‘Subgroup Growth’, where they highlighted the problem as particularly interesting. Dr. Barnea's and Prof. Schlage-Puchta's argument uses geometric ideas involving symmetries of certain graphs called trees (a graph without loops).

The paper, “Branch Groups, Orbit Growth, and Subgroup Growth Types for Pro-p Groups”, was recently published in "Forum of Mathematics, Pi", which is an open access mathematics journal. An open access journal is a journal in which rather than charging readers for reading the papers the journal charges authors for publishing in the journal. This increases the access of researchers from developing countries to cutting edge research.

"Forum of Mathematics, Pi" is a relatively new journal that in a very short time became one of the leading journals in pure mathematics. Indeed, in recent years it has been ranked consistently in the top five pure mathematics journals in terms of citations. This is an encouraging news to those supporting open access journals.

Explore Royal Holloway

Get help paying for your studies at Royal Holloway through a range of scholarships and bursaries.

There are lots of exciting ways to get involved at Royal Holloway. Discover new interests and enjoy existing ones

Heading to university is exciting. Finding the right place to live will get you off to a good start

Whether you need support with your health or practical advice on budgeting or finding part-time work, we can help

Discover more about our 21 departments and schools

Find out why Royal Holloway is in the top 25% of UK universities for research rated ‘world-leading’ or ‘internationally excellent’

Royal Holloway is a research intensive university and our academics collaborate across disciplines to achieve excellence.

Discover world-class research at Royal Holloway

Discover more about who we are today, and our vision for the future

Royal Holloway began as two pioneering colleges for the education of women in the 19th century, and their spirit lives on today

We’ve played a role in thousands of careers, some of them particularly remarkable

Find about our decision-making processes and the people who lead and manage Royal Holloway today