Distributivity and pseudocomplementation of lattices of generalized \(L\)-subgroups
2016 ◽
Vol 5
(2)
◽
pp. 107
◽
Keyword(s):
The main goal of this paper is to study the lattice of \((0,\mu)\)-\(L\)-subgroups of a group. We characterize abelian groups by the lattice of \((0,\mu)\)-\(L\)-subgroups. Also, we show that a group $G$ is locally cyclic if and only if the lattice of \((0,\mu)\)-\(L\)-subgroups is distributive. As consequence, we obtain that the lattices of all \((\in,\in\vee q)\)-fuzzy subgroups and all fuzzy subgroups of a finite cyclic group are distributive. Finally, we study groups which of the lattice of \((\lambda,\mu)\)-\(L\)-subgroups is pseudocomplemented lattice.
Keyword(s):
Keyword(s):
2009 ◽
Vol 2009
◽
pp. 1-12
◽
Keyword(s):
1987 ◽
Vol 39
(4)
◽
pp. 969-982
◽
Keyword(s):
2019 ◽
Vol 19
(02)
◽
pp. 2050040
◽
Keyword(s):
2019 ◽
Vol 28
(11)
◽
pp. 1940006