scholarly journals The minimal generating sets of of size four

2013 ◽  
Vol 16 ◽  
pp. 419-423 ◽  
Author(s):  
Sebastian Jambor
Keyword(s):  
Generating Set ◽  
Generating Sets ◽  
Minimal Generating Set

AbstractWe show that there are only finitely many primes $p$ such that $\mathrm{PSL} (2, p)$ has a minimal generating set of size four.Supplementary materials are available with this article.

A general approach for generating sets of certain subsemigroups of monotone maps

2019 ◽  
Vol 13 (07) ◽  
pp. 2050132
Author(s):  
Leyla Bugay
Keyword(s):  
Natural Order ◽  
Finite Chain ◽  
Generating Set ◽  
Generating Sets ◽  
Monotone Maps ◽  
Minimal Generating Set

Let [Formula: see text] and [Formula: see text] be the monoids of all (full) transformations and of all partial transformations, on a finite chain [Formula: see text] under its natural order, respectively. Moreover, let [Formula: see text] ([Formula: see text]) be the subsemigroup of [Formula: see text] ([Formula: see text]) consists of all monotone transformations (monotone partial transformations) with height less than or equal to [Formula: see text] for [Formula: see text] ([Formula: see text]). In this paper, we develop a new and general approach to find a (minimal) generating set of [Formula: see text] ([Formula: see text]).

scholarly journals Minimal generating sets for some wreath products of groups

1973 ◽  
Vol 9 (1) ◽  
pp. 127-136
Author(s):  
Yeo Kok Chye
Keyword(s):  
Abelian Group ◽  
Nilpotent Group ◽  
Wreath Product ◽  
Wreath Products ◽  
Finitely Generated ◽  
Generating Set ◽  
Generating Sets ◽  
Products Of Groups ◽  
Minimal Generating Set ◽  
Standard Wreath Product

Let d(G) denote the minimum of the cardinalities of the generating sets of the group G. Call a generating set of cardinality d(G) a minimal generating set for G. If A is a finitely generated nilpotent group, B a non-trivial finitely generated abelian group and A wr B is their (restricted, standard) wreath product, then it is proved (by explicitly constructing a minimal generating set for A wr B ) that d(AwrB) = max{l+d(A), d(A×B)} where A × B is their direct product.

scholarly journals Minimal generating sets of directed oriented Reidemeister moves

2017 ◽  
Vol 26 (04) ◽  
pp. 1750016 ◽  
Author(s):  
Piotr Suwara
Keyword(s):  
Generating Set ◽  
Type Formula ◽  
Generating Sets ◽  
Reidemeister Moves ◽  
Different Types ◽  
Minimal Generating Set ◽  
Minimal Formula

Polyak proved that the set [Formula: see text] is a minimal generating set of oriented Reidemeister moves. One may distinguish between forward and backward moves, obtaining [Formula: see text] different types of moves, which we call directed oriented Reidemeister moves. In this paper, we prove that the set of eight directed Polyak moves [Formula: see text] is a minimal generating set of directed oriented Reidemeister moves. We also specialize the problem, introducing the notion of a [Formula: see text]-generating set for a link [Formula: see text]. The same set is proven to be a minimal [Formula: see text]-generating set for any link [Formula: see text] with at least two components. Finally, we discuss knot diagram invariants arising in the study of [Formula: see text]-generating sets for an arbitrary knot [Formula: see text], emphasizing the distinction between ascending and descending moves of type [Formula: see text].

scholarly journals Bounding the maximal size of independent generating sets of finite groups

2020 ◽  
pp. 1-18
Author(s):  
Andrea Lucchini ◽  
Mariapia Moscatiello ◽  
Pablo Spiga
Keyword(s):  
Finite Group ◽  
Finite Groups ◽  
Prime Numbers ◽  
Generating Set ◽  
Generating Sets ◽  
Number Of Generators ◽  
Maximal Size ◽  
A Finite Group ◽  
Minimal Generating Set

Abstract Denote by m(G) the largest size of a minimal generating set of a finite group G. We estimate m(G) in terms of $\sum _{p\in \pi (G)}d_p(G),$ where we are denoting by d p (G) the minimal number of generators of a Sylow p-subgroup of G and by π(G) the set of prime numbers dividing the order of G.

A Control System for a High-Quality Generating Set Equipped With a Two-Shaft Gas Turbine

1991 ◽  
Vol 113 (2) ◽  
pp. 290-295 ◽  
Author(s):  
H. Kumakura ◽  
T. Matsumura ◽  
E. Tsuruta ◽  
A. Watanabe
Keyword(s):  
Control System ◽  
Gas Turbine ◽  
Gas Turbines ◽  
High Quality ◽  
Constant Frequency ◽  
Generating Set ◽  
Generating Sets ◽  
Power Turbine ◽  
Computer Centers ◽  
Supply Systems

A control system has been developed for a high-quality generating set (150-kW) equipped with a two-shaft gas turbine featuring a variable power turbine nozzle. Because this generating set satisfies stringent frequency stability requirements, it can be employed as the direct electric power source for computer centers without using constant-voltage, constant-frequency power supply systems. Conventional generating sets of this kind have normally been powered by single-shaft gas turbines, which have a larger output shaft inertia than the two-shaft version. Good frequency characteristics have also been realized with the two-shaft gas turbine, which provides superior quick start ability and lower fuel consumption under partial loads.

scholarly journals The Fundamental Group of Balanced Simplicial Complexes and Posets

10.37236/73 ◽  
2009 ◽  
Vol 16 (2) ◽  
Author(s):  
Steven Klee
Keyword(s):  
Fundamental Group ◽  
Upper Bound ◽  
Large Family ◽  
Simplicial Complexes ◽  
Generating Set ◽  
Minimal Generating Set

We establish an upper bound on the cardinality of a minimal generating set for the fundamental group of a large family of connected, balanced simplicial complexes and, more generally, simplicial posets.

The Fuzziness of a Minimal Generating Set of Fedorov Groups

2021 ◽  
Vol 66 (6) ◽  
pp. 913-919
Author(s):  
A. M. Banaru ◽  
V. R. Shiroky ◽  
D. A. Banaru
Keyword(s):  
Generating Set ◽  
Minimal Generating Set

The Number of Generators of a Linear p-Group

1972 ◽  
Vol 24 (5) ◽  
pp. 851-858 ◽  
Author(s):  
I. M. Isaacs
Keyword(s):  
Generating Set ◽  
Nilpotence Class ◽  
Number Of Generators ◽  
Minimal Generating Set

Let G be a finite p-group, having a faithful character χ of degree f. The object of this paper is to bound the number, d(G), of generators in a minimal generating set for G in terms of χ and in particular in terms of f. This problem was raised by D. M. Goldschmidt, and solved by him in the case that G has nilpotence class 2.

scholarly journals Triple-crossing projections, moves on knots and links and their minimal diagrams

2020 ◽  
Vol 29 (04) ◽  
pp. 2050015 ◽  
Author(s):  
Michał Jabłonowski ◽  
Łukasz Trojanowski
Keyword(s):  
Triple Point ◽  
Crossing Number ◽  
Systematic Method ◽  
Generating Set ◽  
New Type ◽  
Knots And Links ◽  
Minimal Generating Set

In this paper, we present a systematic method to generate prime knot and prime link minimal triple-point projections, and then classify all classical prime knots and prime links with triple-crossing number at most four. We also extend the table of known knots and links with triple-crossing number equal to five. By introducing a new type of diagrammatic move, we reduce the number of generating moves on triple-crossing diagrams, and derive a minimal generating set of moves connecting triple-crossing diagrams of the same knot.

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