The tunnel number of a PL knot K is the minimum number of PL one-cells which must be attached in order that the regular neighborhood of the resulting complex has complement a handlebody [2]. It is easy to see that n-bridge knots have tunnel numbers (n 1) and torus knots have tunnel number one. More difficult is finding knots which have higher tunnel number. If a knot has tunnel number one, it w...

We study the asymptotic behaviour of a finitely presented Rees quotient S = Inv〈A | ci = 0 (i = 1, . . . , k) 〉 of a free inverse semigroup over a finite alphabet A. It is shown that if the semigroup S has polynomial growth then S is monogenic (with zero) or k ≥ 3. The three relator case is fully characterised, yielding a sequence of two-generated three-relator semigroups whose Gelfand-Kirillov...

By estimating the subgroup numbers associated with various classes of large groups, we exhibit a number of new phenomena in the theory of subgroup growth. Key-words: subgroup growth, large groups, one-relator groups, HNN-extensions MSC-Index: 20E07

It is a well-known fact that every group G has a presentation of the form G = F/R, where F is a free group and R the kernel of the natural epimorphism from F onto G. Driven by the desire to obtain a similar presentation of the group of automorphisms Aut(G), we can consider the subgroup Stab(R) ⊆ Aut(F ) of those automorphisms of F that stabilize R, and try to figure out if the natural homomorph...

In this paper we prove several results regarding decidability ofthe membership problem for certain submonoids in amalgamated free prod-ucts and HNN extensions of groups. These general are then appliedto solve the prefix a number classes one-relatorgroups which low Magnus–Moldavanski i hierarchy. Since pre-fix one-relator groups is intimately related to theword special inverse monoids theE-unita...

Resumo O artigo discute a influência do voto relator na formação da decisão colegiada, considerando as particularidades modelo de colegialidade adotado pelo direito processual civil brasileiro. A partir literatura sobre julgamentos colegiados no Brasil e aportes Psicologia heurísticas vieses cognitivos, foi realizado experimento simulando julgamento caso responsabilidade por erro médico, cujos ...

this paper extends the scope of algebraic computation based on a non standard × to the more basic case of a non standard +, where standard means associative and commutative. two physically meaningful examples of a non standard + are provided by the observation of motion in special relativity, from either outside (3d) or inside (2d or more), we revisit the “gyro”-theory of ungar to present the m...