TY - JOUR
T1 - Recognition of finite matrix groups over infinite fields
AU - Detinko, Alla
AU - Flannery, Dane
AU - O'Brien, Eamonn
PY - 2013/3/1
Y1 - 2013/3/1
N2 - We present a uniform methodology for computing with finitely generated matrix groups over any infinite field. As one application, we completely solve the problem of deciding finiteness in this class of groups. We also present an algorithm that, given such a finite group as input, in practice successfully constructs an isomorphic copy over a finite field, and uses this copy to investigate the group’s structure. Implementations of our algorithms are available in Magma.
AB - We present a uniform methodology for computing with finitely generated matrix groups over any infinite field. As one application, we completely solve the problem of deciding finiteness in this class of groups. We also present an algorithm that, given such a finite group as input, in practice successfully constructs an isomorphic copy over a finite field, and uses this copy to investigate the group’s structure. Implementations of our algorithms are available in Magma.
KW - Finitely generated linear group
KW - Finite linear group
KW - Decision problem
KW - Algorithm
UR - https://www.scopus.com/inward/record.uri?eid=2-s2.0-84870254867&doi=10.1016%2fj.jsc.2012.04.002&partnerID=40&md5=801fd185e1b4cabf8d776c4ba453cc93
U2 - 10.1016/j.jsc.2012.04.002
DO - 10.1016/j.jsc.2012.04.002
M3 - Article
VL - 50
SP - 100
EP - 109
JO - Journal of Symbolic Computation,
JF - Journal of Symbolic Computation,
ER -