Profinite Groups Associated to Sofic Shifts Are Free
نویسندگان
چکیده
We show that the maximal subgroup of the free profinite semigroup associated by Almeida to an irreducible sofic shift is a free profinite group, generalizing an earlier result of the second author for the case of the full shift (whose corresponding maximal subgroup is the maximal subgroup of the minimal ideal). A corresponding result is proved for certain relatively free profinite semigroups. We also establish some other analogies between the kernel of the free profinite semigroup and the J -class associated to an irreducible sofic shift.
منابع مشابه
Sofic groups and profinite topology on free groups
We give a definition of weakly sofic groups (w-sofic groups). Our definition is rather natural extension of the definition of sofic groups where instead of Hamming metric on symmetric groups we use general bi-invariant metrics on finite groups. The existence of non w-sofic groups is equivalent to some conjecture about profinite topology on free groups.
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We give a definition of weakly sofic groups (w-sofic groups). Our definition is a rather natural extension of the definition of sofic groups where instead of the Hamming metric on symmetric groups we use general bi-invariant metrics on finite groups. The existence of non w-sofic groups is equivalent to a profinite topology property of products of conjugacy classes in free groups.
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It is given a structural conjugacy invariant in the set of pseudowords whose finite factors are factors of a given subshift. Some profinite semigroup tools are developed for this purpose. With these tools a shift equivalence invariant of sofic subshifts is obtained, improving an invariant introduced by Béal, Fiorenzi and Perrin using different techniques. This new invariant is used to prove tha...
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متن کاملREFERENCES TO THE COURSE ”FINITE-DIMENSIONAL APPROXIMATION PROPERTIES OF FINITE GROUPS” References
[4] Lev Glebsky and Luis Manuel Rivera, Sofic groups and profinite topology on free groups, J. Algebra 320 (2008), no. 9, 3512-3518. [2] Misha Gromov, Endomorphisms of symbolic algebraic varieties, J. Eur. Math. Soc. (JEMS) 1 (1999), no. 2, 109-197. [3] Gábor Elek and Endre Szabó, Hyperlinearity, essentially free actions and Linvariants. The sofic property, Math. Ann. 332 (2005), no. 2, 421-441...
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