On some metabelian 2-groups and applications III

2016 ◽  
Vol 09 (04) ◽  
pp. 1650072
Author(s):  
Abdelkader Zekhnini ◽  
Abdelmalek Azizi ◽  
Mohammed Taous
Keyword(s):  
Number Theory ◽  
Group Theory ◽  
Theoretical Results

The capitulation problem is one of the most important topic in number theory, and as it is closely related to the group theory, we present, in this paper, some group theoretical results to solve this problem, in a particular case, whenever [Formula: see text] for some metabelian [Formula: see text]-group [Formula: see text]. Then we illustrate our results by some examples.

Parametrizing Fuchsian Subgroups of the Bianchi Groups

1991 ◽  
Vol 43 (1) ◽  
pp. 158-181 ◽  
Author(s):  
C. Maclachlan ◽  
A. W. Reid
Keyword(s):  
Number Theory ◽  
Group Theory ◽  
Present Article ◽  
Ring Of Integers ◽  
Low Dimensional Topology ◽  
Low Dimensional

Let dbe a positive square-free integer and let Od denote the ring of integers in . The groups PSL2(Od) are collectively known as the Bianchi groups and have been widely studied from the viewpoints of group theory, number theory and low-dimensional topology. The interest of the present article is in geometric Fuchsian subgroups of the groups PSL2(Od). Clearly PSL2 is such a subgroup; however results of [18], [19] show that the Bianchi groups are rich in Fuchsian subgroups.

Low Reynolds number heat transfer from a circular cylinder

1968 ◽  
Vol 32 (1) ◽  
pp. 21-28 ◽  
Author(s):  
C. A. Hieber ◽  
B. Gebhart
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Number Theory ◽  
Circular Cylinder ◽  
Prandtl Number ◽  
Experimental Work ◽  
Reynolds Numbers ◽  
Low Reynolds Numbers ◽  
Low Reynolds ◽  
Theoretical Results

Theoretical results are obtained for forced heat convection from a circular cylinder at low Reynolds numbers. Consideration is given to the cases of a moderate and a large Prandtl number, the analysis in each case being based upon the method of matched asymptotic expansions. Comparison between the moderate Prandtl number theory and known experimental results indicates excellent agreement; no relevant experimental work has been found for comparison with the large Prandtl number theory.

scholarly journals On the Clifford collineation, transform and similarity groups. I.

1961 ◽  
Vol 2 (1) ◽  
pp. 60-79 ◽  
Author(s):  
Beverley Bolt ◽  
T. G. Room ◽  
G. E. Wall
Keyword(s):  
Number Theory ◽  
Group Theory ◽  
Similarity Groups ◽  
Clifford Groups

Papers I, II of this projected series lay the algebraic foundations of the theory of the Clifford groups; I deals with the casep> 2, II with the casep= 2. The present introduction refers to both papers. Our theory has applications in group theory, geometry and number theory.

The Applications of Group Theory

2012 ◽  
Vol 430-432 ◽  
pp. 1265-1268
Author(s):  
Xiao Qiang Guo ◽  
Zheng Jun He
Keyword(s):  
Number Theory ◽  
Algebraic Geometry ◽  
Group Theory ◽  
Algebraic Number ◽  
Algebraic Topology ◽  
Polynomial Equation ◽  
Algebraic Number Theory ◽  
Simple Groups ◽  
Finite Simple Groups

Since the classification of finite simple groups completed last century, the applications of group theory are more and more widely. We first introduce the connection of groups and symmetry. And then we respectively introduce the applications of group theory in polynomial equation, algebraic topology, algebraic geometry , cryptography, algebraic number theory, physics and chemistry.

Preliminaries

2020 ◽  
pp. 5-56
Author(s):  
Andreas Bolfing
Keyword(s):  
Field Theory ◽  
Number Theory ◽  
Group Theory ◽  
Complexity Theory ◽  
Prime Numbers ◽  
Ring Theory ◽  
Cryptographic Primitives ◽  
Mathematical Concepts ◽  
Cyclic Groups ◽  
Efficiency Of Algorithms

Blockchains are heavily based on mathematical concepts, in particular on algebraic structures. This chapter starts with an introduction to the main aspects in number theory, such as the divisibility of integers, prime numbers and Euler’s totient function. Based on these basics, it follows a very detailed introduction to modern algebra, including group theory, ring theory and field theory. The algebraic main results are then applied to describe the structure of cyclic groups and finite fields, which are needed to construct cryptographic primitives. The chapter closes with an introduction to complexity theory, examining the efficiency of algorithms.

The Matrix Equations A = XYZ And B = ZYX and Related Ones

1974 ◽  
Vol 17 (2) ◽  
pp. 179-183 ◽  
Author(s):  
J. L. Brenner ◽  
M. J. S. Lim
Keyword(s):  
Group Theory ◽  
Matrix Theory ◽  
Necessary Condition ◽  
Matrix Equations ◽  
General Group ◽  
Matrix Groups ◽  
The Matrix ◽  
Theory Application ◽  
Theoretical Results

In [15], O. Taussky-Todd posed the problem of title, namely to find X, Y, Z when A, B are given. Clearly if X, Y, Z exist then A, B are either both invertible or both noninvertible.In section 1, the problem is reviewed in case A, B are both invertible. The problem is seen to be fundamentally one of group theory rather than matrix theory. Application of results of Shoda, Thompson, Ree to the general group-theoretical results allows specialization to certain matrix groups.In Section 2, examples and counterexamples are given in case A, B are noninvertible. A general necessary condition for solvability (involving ranks) is obtained. This condition may or may not be sufficient. For dim A=2, 3 the problem is settled: there is always a solution in the noninvertible case.

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