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Quantifying Residual Finiteness
"... We introduce the notion of quantifying the extent to which a finitely generated group is residually finite. We investigate this behavior for examples that include free groups, the first Grigorchuk group, finitely generated nilpotent groups, and certain arithmetic groups such as SLn(Z). In the contex ..."
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Cited by 23 (7 self)
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We introduce the notion of quantifying the extent to which a finitely generated group is residually finite. We investigate this behavior for examples that include free groups, the first Grigorchuk group, finitely generated nilpotent groups, and certain arithmetic groups such as SLn
Residual finite state automata

, 2002
"... We define a new variety of Non Deterministic Automata: a Residual Finite State Automata is a NFA all the states of which define residual languages of the language it recognizes. We prove that every regular language is recognized by a unique (canonical) RFSA which has a minimal number of states and a ..."
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Cited by 16 (5 self)
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We define a new variety of Non Deterministic Automata: a Residual Finite State Automata is a NFA all the states of which define residual languages of the language it recognizes. We prove that every regular language is recognized by a unique (canonical) RFSA which has a minimal number of states
ARBITRARILY LARGE RESIDUAL FINITENESS GROWTH
"... Abstract. The residual finiteness growth of a group quantifies how well approximated the group is by its finite quotients. In this paper, we construct groups with arbitrarily large residual finiteness growth. We also demonstrate a new relationship between residual finiteness growth and some decisio ..."
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Cited by 5 (2 self)
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Abstract. The residual finiteness growth of a group quantifies how well approximated the group is by its finite quotients. In this paper, we construct groups with arbitrarily large residual finiteness growth. We also demonstrate a new relationship between residual finiteness growth and some
Residual Finite Tree Automata
 In Proceedings of the seventh int. conf. developments in Language Theory DLT’03, number 2710 in Lecture Notes in Computer Science
, 2003
"... Tree automata based algorithms are essential in many fields in computer science such as verification, specification, program analysis. They become also essential for databases with... ..."
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Cited by 7 (1 self)
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Tree automata based algorithms are essential in many fields in computer science such as verification, specification, program analysis. They become also essential for databases with...
Nonlinear residually finite groups
 J. Algebra
"... We prove that groups 〈a, b, t  tat −1 = a k, tbt −1 = b l 〉 are not linear provided k, l ̸∈ {−1, 1}. As a consequence we obtain the first example of a nonlinear residually finite 1related group. 1 ..."
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Cited by 8 (1 self)
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We prove that groups 〈a, b, t  tat −1 = a k, tbt −1 = b l 〉 are not linear provided k, l ̸∈ {−1, 1}. As a consequence we obtain the first example of a nonlinear residually finite 1related group. 1
RESIDUALLY FINITE VARIETIES OF NONASSOCIATIVE ALGEBRAS
"... We prove that if V is a residually finite variety of nonassociative algebras over a finite field, and the enveloping algebra of each finite member of V is finitely generated as a module over its center, then V is generated by a single finite algebra. ..."
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We prove that if V is a residually finite variety of nonassociative algebras over a finite field, and the enveloping algebra of each finite member of V is finitely generated as a module over its center, then V is generated by a single finite algebra.
On a Class of Residually Finite Groups
, 2003
"... Let kn, be positive integers and kttt,,, 10 … be nonzero integers. We denote by)(nWk the class of groups G in which, for every subset X of G of cardinality 1+n, there exist a subset XX ⊆0, with,12 0 +≤ ≤ nX, and a function 0},,2,1,0{: Xkf → … , with)1()0 ( ff ≠ such that 1],,, [ 10 10 =ktktt ..."
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Cited by 1 (1 self)
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=ktktt xxx … where)(: ifxi = , ki,,1,0 … =. The class)( * nWk is defined exactly as)(nWk, with additional conditions “ Hx j ∈ whenever Hx jtj ∈, where GHx jtj ≤ ≠ ”. Let G be a finitely generated residually finite group. Here we prove that (1) If)(nWG k ∈ , then G has a normal nilpotent subgroup N
Residual finiteness growths of virtually special groups
"... Abstract. Let G be a virtually special group. Then the residual finiteness growth of G is at most linear. This result cannot be found by embedding G into a special linear group. Indeed, the special linear group SLk(Z), for k> 2, has residual finiteness growth nk−1. ..."
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Cited by 1 (0 self)
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Abstract. Let G be a virtually special group. Then the residual finiteness growth of G is at most linear. This result cannot be found by embedding G into a special linear group. Indeed, the special linear group SLk(Z), for k> 2, has residual finiteness growth nk−1.
Residually finite dimensional and AFembeddable C∗algebras
, 2000
"... We show that every separable nuclear residually finite dimensional Calgebras satisfying the Universal Coefficient Theorem can be embedded into a unital separable simple AFalgebra. ..."
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Cited by 3 (0 self)
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We show that every separable nuclear residually finite dimensional Calgebras satisfying the Universal Coefficient Theorem can be embedded into a unital separable simple AFalgebra.
Results 1  10
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3,031