Hall's universal group has ample generic automorphisms

2019 ◽  
Vol 65 (2) ◽  
pp. 205-211
Author(s):  
Shichang Song
Keyword(s):  
Universal Group

scholarly journals A correspondence between a class of monoids and self-similar group actions II

2015 ◽  
Vol 25 (04) ◽  
pp. 633-668
Author(s):  
Mark V. Lawson ◽  
Alistair R. Wallis
Keyword(s):  
Group Actions ◽  
Similar Group ◽  
Universal Group ◽  
Length Functions ◽  
Group Of Units ◽  
Hnn Extensions ◽  
Hnn Extension ◽  
Self Similar ◽  
Cancellative Monoids

The first author showed in a previous paper that there is a correspondence between self-similar group actions and a class of left cancellative monoids called left Rees monoids. These monoids can be constructed either directly from the action using Zappa–Szép products, a construction that ultimately goes back to Perrot, or as left cancellative tensor monoids from the covering bimodule, utilizing a construction due to Nekrashevych. In this paper, we generalize the tensor monoid construction to arbitrary bimodules. We call the monoids that arise in this way Levi monoids and show that they are precisely the equidivisible monoids equipped with length functions. Left Rees monoids are then just the left cancellative Levi monoids. We single out the class of irreducible Levi monoids and prove that they are determined by an isomorphism between two divisors of its group of units. The irreducible Rees monoids are thereby shown to be determined by a partial automorphism of their group of units; this result turns out to be significant since it connects irreducible Rees monoids directly with HNN extensions. In fact, the universal group of an irreducible Rees monoid is an HNN extension of the group of units by a single stable letter and every such HNN extension arises in this way.

VERIFYING THAT A GROUP IS VIRTUALLY FREE

1991 ◽  
Vol 01 (03) ◽  
pp. 339-351
Author(s):  
ROBERT H. GILMAN
Keyword(s):  
Finite Index ◽  
Free Subgroup ◽  
Universal Group ◽  
Finitely Presented Groups ◽  
Finite Presentation ◽  
Finitely Presented

This paper is concerned with computation in finitely presented groups. We discuss a procedure for showing that a finite presentation presents a group with a free subgroup of finite index, and we give methods for solving various problems in such groups. Our procedure works by constructing a particular kind of partial groupoid whose universal group is isomorphic to the group presented. When the procedure succeeds, the partial groupoid can be used as an aid to computation in the group.

scholarly journals COMPARATIVE QUALITY ASSESSMENT OF ROOT CANAL PREPARATION WITH DIFFERENT SYSTEMS OF ENDODONTIC INSTRUMENTS

2020 ◽  
Vol 73 (6) ◽  
pp. 1145-1148
Author(s):  
Maryna A. Goray ◽  
Nataliia G. Gadzhula ◽  
Olena V. Muntian ◽  
Olena L. Cherepakha ◽  
Larysa F. Kurdysh
Keyword(s):  
Root Canal ◽  
Canal System ◽  
Universal Group ◽  
Root Canals ◽  
Root Canal System ◽  
High Degree ◽  
Dentine Surface ◽  
Apical Area

The aim: To compare the quality of root canal system preparation with the use of manual K-files, machine Protaper Universal and Silk files by in vitro studies. Materials and methods: Root canals preparation in 45 extracted premolars was performed in three groups with 15 teeth in each with K-files, Protaper Universal and Silk files. Transverse sections of the dental root were prepared. Histologically were assessed: amount of sawdust and predentin remaining, the purity degree of root canal walls. Results: When calculating the sawdust amount at the distance of 3 mm from an apex, a high degree of contamination was observed in the manual K-file group: 53.3% versus 33.3% in the Protaper Universal group and against 20.0% in the Silk file group. The amount of predentin after root canal treatment with manual files reached 25-30%. At the distance of 5 mm from the apex the root canals with high and medium purity degree were detected in 86.7% with Silk files and 80.0% with Protaper Universal files used. All predentin was removed when working with Protaper Universal and Silk files. Conclusions: In the histological sections of the root canals treated with K-files, the larger amount of dentine particles and predentin has been revealed than when using machine tools. The largest amount of predentin and dentine were removed with Protaper Universal files. Silk endodontic system is better for treatment of the root canals dentine surface in the apical area compared to Protaper Universal and K-files.

scholarly journals Parabolically induced unitary representations of the universal group $U(F)^+$ are $C_0$

2019 ◽  
Vol 125 (1) ◽  
pp. 113-134
Author(s):  
Corina Ciobotaru
Keyword(s):  
Unitary Representations ◽  
Universal Group

We prove that all parabolically induced unitary representations of the Burger-Mozes universal group $U(F)^{+}$, with $F$ being primitive, are $C_0$. This generalizes the same well-known result for the universal group $U(F)^{+}$, when $F$ is $2$-transitive.

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