[PDF] Top 20 Algorithms for polycyclic by finite groups
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Algorithms for polycyclic by finite groups
... finite and solvable, and so, one may produce a consistent power-conjugate pre- sentation defining it using the method of Subsection 3. The existing methods for computing Sylow subgroups in finite solvable ... See full document
23
Algorithms for polycyclic by finite groups
... of groups (see Chandler and Magnus, 1982). The class of polycyclic-by-finite groups, however, is a subclass of the class of finitely presented groups that possess solvable conjugacy ... See full document
256
Length-based attacks in polycyclic groups
... the algorithms: the length of each random element is in the interval [𝐿 1 , 𝐿 2 ] = [10, 13] , Alice’s private key is the product of 10 elements and the length of both public sets are 𝑁 1 = 𝑁 2 = 20 ...same ... See full document
12
Computing automorphism groups and isomorphism testing in finite groups
... three algorithms have been implemented in MAGMA [BCP97]; the soluble group procedure is written in ‘C’, and the general and p-group algorithms in the MAGMA ...p-group algorithms are also available as ... See full document
121
Locally graded groups with a condition on infinite subsets
... all polycyclic groups, S the class of all soluble groups, R the class of all residually finite groups, L the class of all locally graded groups, N 2 the class of all nilpotent ... See full document
7
The homological functors of some finite two-generator two-groups of nilpotency class two
... of Groups, Algorithms and Programming (GAP) software in the computation of the ...some finite two-generator two-groups of nilpotency class two of Type 3 are provided in this ... See full document
20
Central extensions of polycyclic groups
... are polycyclic groups. A polycyclic g ro u p is c h a ra c te r ized by th e ex istence of a su b n o rm a l series of su b g ro u p s w ith cyclic fa c to r grou p ...soluble groups are ... See full document
110
Bieberbach groups with finite point groups
... Crystallographic AlgoRithms And Tables (CARAT) [7] and the computation of the nonabelian tensor squares of the groups with the Groups, Algrorithms, and Programming (GAP) software [8] lead us first to ... See full document
23
Applications of Lie methods to computations with polycyclic groups
... of finite polycycli- cally presented groups of very large order, see for example ...In finite polycyclically presented groups Cftl benefits from the fact that all relative orders are ... See full document
94
Refined solvable presentations for polycyclic groups
... any finite presentation of a polycyclic group, the polycyclic quotient algorithm [13,14] allows one to compute a polycyclic presentation defining the same ...the polycyclic group is ... See full document
17
Groups whose proper subgroups of infinite rank have polycyclic-by-finite conjugacy classes
... non-trivial finite or abelian factor ...are finite cyclic extensions of divisible abelian p-groups of finite rank, where p is a prime, hence they are Chernikov ...for groups having a ... See full document
7
Sylow multiplicities in finite groups
... It is not difficult to prove that the property τ -unique1 is also inherited by normal subgroups, but at present there is no analog statement concerning quotient groups. Given that, the condition of part (a) of ... See full document
8
A characterization of supersolubility of finite groups
... Theorem . Let F be a saturated formation containing all supersoluble groups. A group G ∈ F if and only if there exists a normal subgroup E of G such that G/E ∈ F and for every non-cyclic Sylow subgroup P of F * ... See full document
6
Finite BCI-groups are solvable
... Abstract. Let S be a subset of a finite group G. The bi-Cayley graph BCay(G, S) of G with respect to S is an undirected graph with vertex set G × {1, 2} and edge set {{(x, 1), (sx, 2)} | x ∈ G, s ∈ S }. A ... See full document
6
On metacyclic subgroups of finite groups
... In the second part of the article, we are concerned with the influence of 2-generator subgroups on the structure of a group. The basic idea behind the results is the following: assume that a group G has 2-generator ... See full document
5
On excess in finite Coxeter groups
... This paper is arranged as follows. Our next section gathers together relevant background material while reviewing much of the standard notation used for Coxeter groups. Theorems 1.1 and 1.2 are established in ... See full document
16
Symmetric generation of finite groups
... CHAPTER TWO: SYMMETRIC REPRESENTATION OF L 2(ll) ELEMENTS Introduction ... 25[r] ... See full document
255
Generation problems for finite groups
... of groups that do and do not have property B we sought to high- light how rare groups with property B ...dihedral groups, showing that all dihedral groups of order 2p n have prop- erty B, for ... See full document
110
Finite groups are big as semigroups
... a finite group G occurs as a maximal proper subsemigroup of an infinite semigroup (in the terminology of Freese, Jeˇ zek and Nation, G is a big semigroup) if and only if |G| ≥ ...any finite semigroup whose ... See full document
10
On the total character of finite groups
... It is a consequence of a well known theorem due to Burnside and Brauer ([7, Theorem 4.3]) that, the total character of the group G is a constituent of 1 + χ + · · · + χ m−1 if χ is a faithful character which takes ... See full document
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