TY - JOUR
T1 - Logical generation of groups
AU - Abdollahi, Alireza
AU - Shahryari, Mohammad
N1 - Publisher Copyright:
© 2024 Taylor & Francis Group, LLC.
PY - 2024/2/28
Y1 - 2024/2/28
N2 - A group G is called logically generated by a subset S, if every element of G can be defined by a first order formula with parameters from S. We consider the case where G is a direct product of finite nilpotent groups with mutually coprime orders and we show that logical and algebraic generations are equivalent in G. We also prove that in the case when G is a free non-abelian group, if S logically generates G then either it generates G algebraically or (Formula presented.) is not a free factor of G.
AB - A group G is called logically generated by a subset S, if every element of G can be defined by a first order formula with parameters from S. We consider the case where G is a direct product of finite nilpotent groups with mutually coprime orders and we show that logical and algebraic generations are equivalent in G. We also prove that in the case when G is a free non-abelian group, if S logically generates G then either it generates G algebraically or (Formula presented.) is not a free factor of G.
KW - Definability
KW - elementary extensions
KW - logical generation
KW - logically cyclic groups
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UR - https://www.mendeley.com/catalogue/27c2f616-808a-35e0-b8fb-6058dbb0b957/
U2 - 10.1080/00927872.2024.2320811
DO - 10.1080/00927872.2024.2320811
M3 - Article
AN - SCOPUS:85186567438
SN - 0092-7872
JO - Communications in Algebra
JF - Communications in Algebra
ER -