TY - JOUR
T1 - Algebraic properties of Riordan subgroups
AU - Barry, Paul
AU - Hennessy, Aoife
AU - Pantelidis, Nikolaos
N1 - Publisher Copyright:
© 2020, Springer Science+Business Media, LLC, part of Springer Nature.
PY - 2021/6
Y1 - 2021/6
N2 - We present properties of the group structure of Riordan arrays. We examine similar properties among known Riordan subgroups, and from this, we define H[r, s, p], a family of Riordan arrays. We generalize conditions for involutions, and pseudo-involutions of H[r, s, p], and we present stabilizers of this family. We find abelian subgroups as intersections of Riordan subgroups and show some alternative semi-direct products of the Riordan group.
AB - We present properties of the group structure of Riordan arrays. We examine similar properties among known Riordan subgroups, and from this, we define H[r, s, p], a family of Riordan arrays. We generalize conditions for involutions, and pseudo-involutions of H[r, s, p], and we present stabilizers of this family. We find abelian subgroups as intersections of Riordan subgroups and show some alternative semi-direct products of the Riordan group.
KW - Involution
KW - Isomorphism
KW - Pseudo-involution
KW - Riordan subgroup
KW - Semi-direct product
KW - Stabilizer
UR - http://www.scopus.com/inward/record.url?scp=85086455540&partnerID=8YFLogxK
U2 - 10.1007/s10801-020-00953-4
DO - 10.1007/s10801-020-00953-4
M3 - Article
AN - SCOPUS:85086455540
SN - 0925-9899
VL - 53
SP - 1015
EP - 1036
JO - Journal of Algebraic Combinatorics
JF - Journal of Algebraic Combinatorics
IS - 4
ER -