Integrals of groups

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

doi:10.1007/s11856-019-1926-y

Integrals of groups

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

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

Abstract

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 language	English
Pages (from-to)	149-178
Number of pages	30
Journal	Israel Journal of Mathematics
Volume	234
Issue number	1
DOIs	https://doi.org/10.1007/s11856-019-1926-y
Publication status	Published - 1 Oct 2019

Access to Document

10.1007/s11856-019-1926-y

Cite this

@article{a69dcd360b3e42518662030229cb2685,

title = "Integrals of groups",

abstract = "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",

author = "Jo{\~a}o Ara{\'u}jo and Cameron, {Peter J.} and Carlo Casolo and Francesco Matucci",

note = "Sem PDF conforme despacho.",

year = "2019",

month = oct,

day = "1",

doi = "10.1007/s11856-019-1926-y",

language = "English",

volume = "234",

pages = "149--178",

journal = "Israel Journal of Mathematics",

issn = "0021-2172",

publisher = "Springer New York",

number = "1",

}

TY - JOUR

T1 - Integrals of groups

AU - Araújo, João

AU - Cameron, Peter J.

AU - Casolo, Carlo

AU - Matucci, Francesco

N1 - Sem PDF conforme despacho.

PY - 2019/10/1

Y1 - 2019/10/1

N2 - 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

AB - 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

UR - http://www.scopus.com/inward/record.url?scp=85073928950&partnerID=8YFLogxK

U2 - 10.1007/s11856-019-1926-y

DO - 10.1007/s11856-019-1926-y

M3 - Article

AN - SCOPUS:85073928950

SN - 0021-2172

VL - 234

SP - 149

EP - 178

JO - Israel Journal of Mathematics

JF - Israel Journal of Mathematics

IS - 1

ER -

Integrals of groups

Abstract

Access to Document

Other files and links

Fingerprint

Cite this