TY - JOUR
T1 - ON PROFINITE POLYADIC GROUPS
AU - Shahryari, Mohammad
AU - Rostami, Mohsen
N1 - Publisher Copyright:
© (2023), (Sobolev Institute of Mathematics). Shahryari M., Rostami M.
PY - 2023
Y1 - 2023
N2 - We study the structure of profinite polyadic groups and we prove that a polyadic topological group (G, f) is profinite, if and only if, it is compact, Hausdorff, totally disconnected. More generally, for a pseudo-variety (or a formation) of finite groups X, we define the class of X-polyadic groups, and we show that a polyadic group (G, f) is pro-X, if and only if, it is compact, Hausdorff, totally disconnected and for every open congruence R, the quotient (G/R, fR) is X-polyadic.
AB - We study the structure of profinite polyadic groups and we prove that a polyadic topological group (G, f) is profinite, if and only if, it is compact, Hausdorff, totally disconnected. More generally, for a pseudo-variety (or a formation) of finite groups X, we define the class of X-polyadic groups, and we show that a polyadic group (G, f) is pro-X, if and only if, it is compact, Hausdorff, totally disconnected and for every open congruence R, the quotient (G/R, fR) is X-polyadic.
KW - Polyadic groups
KW - Post’s cover and retract of a polyadic group
KW - Profinite groups and polyadic groups
KW - n-ary groups
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U2 - 10.33048/semi.2023.20.048
DO - 10.33048/semi.2023.20.048
M3 - Article
AN - SCOPUS:85170635922
SN - 1813-3304
VL - 20
SP - 814
EP - 823
JO - Siberian Electronic Mathematical Reports
JF - Siberian Electronic Mathematical Reports
IS - 2
ER -