Integrals of groups

João Araújo, Peter J. Cameron, Carlo Casolo, Francesco Matucci

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


An integral of a group G is a group H whose derived group (commutator subgroup) is isomorphic to G. This paper discusses integrals of groups, and in particular questions about which groups have integrals and how big or small those integrals can be. Our main results are:If a finite group has an integral, then it has a finite integral.A precise characterization of the set of natural numbers n for which every group of order n is integrable: these are the cubefree numbers n which do not have prime divisors p and q with q

Original languageEnglish
Pages (from-to)149-178
Number of pages30
JournalIsrael Journal of Mathematics
Issue number1
Publication statusPublished - 1 Oct 2019


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