On locally finite groups whose derived subgroup is locally nilpotent
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DOI: 10.1002/mana.202400263
Abstract: A celebrated theorem of Helmut Wielandt shows that the nilpotent residual of the subgroup generated by two subnormal subgroups of a finite group is the subgroup generated by the nilpotent residuals of the subgroups. This… read more here.
Keywords: locally nilpotent; finite groups; derived subgroup; subgroup generated ... See more keywords
Ground state solutions for asymptotically linear Schrödinger equations on locally finite graphs
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DOI: 10.1002/mma.10145
Abstract: We are considered with the following nonlinear Schrödinger equation: −Δu+(λa(x)+1)u=f(u),x∈V,$$ -\Delta u+\left(\lambda a(x)+1\right)u=f(u),x\in V, $$ on a locally finite graph G=(V,E)$$ G=\left(V,E\right) $$ , where V$$ V $$ denotes the vertex set, E$$ E $$… read more here.
Keywords: schr dinger; asymptotically linear; state; ground state ... See more keywords
Dirichlet Spaces Associated with Locally Finite Rooted Directed Trees
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DOI: 10.1007/s00020-017-2400-z
Abstract: Let $$\mathscr {T}=(V, \mathcal E)$$T=(V,E) be a leafless, locally finite rooted directed tree. We associate with $$\mathscr {T}$$T a one parameter family of Dirichlet spaces $$\mathscr {H}_q~(q \geqslant 1)$$Hq(q⩾1), which turn out to be Hilbert… read more here.
Keywords: directed trees; dirichlet spaces; rooted directed; finite rooted ... See more keywords
The Curious Spectra and Dynamics of Non-locally Finite Crystals
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DOI: 10.1007/s00220-025-05346-x
Abstract: This paper is devoted to the investigation of the spectral theory and dynamical properties of periodic graphs which are not locally finite but carry non-negative, symmetric and summable edge weights. These graphs are shown to… read more here.
Keywords: spectra dynamics; non locally; curious spectra; finite crystals ... See more keywords
On the Relationships Between Central Series in Some Locally Finite Groups
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DOI: 10.1007/s11253-017-1318-6
Abstract: It is shown that the class of locally finite divisible-by-bounded groups is both a Schur class and a Baer class. read more here.
Keywords: relationships central; finite groups; series locally; class ... See more keywords
On images of locally finite derivations and E-derivations
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DOI: 10.1016/j.jpaa.2018.07.002
Abstract: Abstract Some cases of the LFED Conjecture, proposed by the second author [15] , for certain integral domains are proved. In particular, the LFED Conjecture is completely established for the field of fractions k (… read more here.
Keywords: derivations derivations; locally finite; images locally; lfed conjecture ... See more keywords
Quantum Automorphism Groups of Connected Locally Finite Graphs and Quantizations of Discrete Groups
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DOI: 10.1093/imrn/rnad099
Abstract: We construct for every connected locally finite graph $\Pi $ the quantum automorphism group $\operatorname{QAut} \Pi $ as a locally compact quantum group. When $\Pi $ is vertex transitive, we associate to $\Pi $ a… read more here.
Keywords: quantum automorphism; group; finite graphs; operatorname qaut ... See more keywords
Subgroups, of Chevalley groups over a locally finite field, defined by a family of additive subgroups
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DOI: 10.1134/s0001434617110190
Abstract: It is proved that every elementary carpet of nonzero additive subgroups which is associated with a Chevalley group of a Lie rank exceeding one over a locally finite field coincides, up to conjugation by a… read more here.
Keywords: finite field; field; additive subgroups; chevalley groups ... See more keywords