TY - JOUR
T1 - Common transversals and complements in abelian groups
AU - Aivazidis, S.
AU - Loukaki, M.
AU - Sambale, B.
N1 - Funding Information:
Open access funding provided by HEAL-Link Greece. The first author is supported by the Hellenic Foundation for Research and Innovation, Project HFRI-FM17-1733. The third author is supported by the German Research Foundation (SA 2864/4-1).
PY - 2024/5
Y1 - 2024/5
N2 - Given a finite abelian group G and cyclic subgroups A, B, C of G of the same order, we find necessary and sufficient conditions for A, B, C to admit a common transversal for the cosets they afford. For an arbitrary number of cyclic subgroups, we give a sufficient criterion when there exists a common complement. Moreover, in several cases where a common transversal exists, we provide concrete constructions.
AB - Given a finite abelian group G and cyclic subgroups A, B, C of G of the same order, we find necessary and sufficient conditions for A, B, C to admit a common transversal for the cosets they afford. For an arbitrary number of cyclic subgroups, we give a sufficient criterion when there exists a common complement. Moreover, in several cases where a common transversal exists, we provide concrete constructions.
KW - 05D15
KW - 05E16
KW - 20D60
KW - Common complements
KW - Finite abelian groups
KW - Transversals
UR - http://www.scopus.com/inward/record.url?scp=85187259921&partnerID=8YFLogxK
U2 - 10.48550/arXiv.2308.06559
DO - 10.48550/arXiv.2308.06559
M3 - Article
AN - SCOPUS:85187259921
VL - 59
SP - 581
EP - 595
JO - Journal of algebraic combinatorics
JF - Journal of algebraic combinatorics
SN - 0925-9899
IS - 3
ER -