TY - JOUR
T1 - Simple polyadic groups
AU - Khodabandeh, H.
AU - Shahryari, M.
PY - 2014/7
Y1 - 2014/7
N2 - The main aim of this article is to establish a characterization of simple polyadic groups in terms of ordinary groups and their automorphisms. We give two different definitions of simpleness for polyadic groups, from the point of views of universal algebra, UAS (universal algebraic simpleness), and group theory, GTS (group theoretical simpleness). We obtain necessary and sufficient conditions for a polyadic group to be UAS or GTS.
AB - The main aim of this article is to establish a characterization of simple polyadic groups in terms of ordinary groups and their automorphisms. We give two different definitions of simpleness for polyadic groups, from the point of views of universal algebra, UAS (universal algebraic simpleness), and group theory, GTS (group theoretical simpleness). We obtain necessary and sufficient conditions for a polyadic group to be UAS or GTS.
KW - congruence
KW - n-ary group
KW - polyadic group
KW - retract of n-ary group
KW - simple polyadic group
UR - http://www.scopus.com/inward/record.url?scp=84906514266&partnerID=8YFLogxK
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U2 - 10.1134/S0037446614040156
DO - 10.1134/S0037446614040156
M3 - Article
AN - SCOPUS:84906514266
SN - 0037-4466
VL - 55
SP - 734
EP - 744
JO - Siberian Mathematical Journal
JF - Siberian Mathematical Journal
IS - 4
ER -