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Page 1877 of Mathematical Reviews Vol. , Issue 2004c [page]

2004 Mathematical Reviews  
Since s is also generally small, this means that the running time of a nearly linear-time algorithm on a small-base group with small generating set is O(ng(logn)), for a polynomial g.  ...  In Chapters 5 and 6, a large number of nearly linear-time algorithms for carrying out structural computations within G are described.  ... 

Page 6726 of Mathematical Reviews Vol. , Issue 92m [page]

1992 Mathematical Reviews  
This paper describes an algorithm for computing a Sylow p- subgroup of a finite permutation group G; an implementation now exists in the CAYLEY system.  ...  The basic idea is to find an element g of order p that is central in a Sylow p-subgroup, to compute C = C¢(g) (which contains the required Sylow subgroup), and then to apply the algorithm recursively to  ... 

Page 2188 of Mathematical Reviews Vol. , Issue 98D [page]

1998 Mathematical Reviews  
Liebeck (4-LNDIC; London) 98d:20003 20B40 20D05 68Q25 Morje, Prabhay (1-OHS; Columbus, OH) On nearly linear time algorithms for Sylow subgroups of small-base permutation groups.  ...  For small-base permutation groups, this running time becomes nearly linear, O(snlog‘’n). If the order of G is known in advance then the algorithms can be upgraded to Las Vegas algorithms.  ... 

Page 3272 of Mathematical Reviews Vol. , Issue 2000e [page]

2000 Mathematical Reviews  
when the group is of small base, i.e., log|G| < log‘ n for some fixed constant c.  ...  Namely, find Sylow subgroups in the simple factors in a composition series and paste them together to a Sylow subgroup of the entire group.  ... 

Group isomorphism is nearly-linear time for most orders [article]

Heiko Dietrich, James B. Wilson
2021 arXiv   pre-print
We show that there is a dense set ⊆ℕ of group orders and a constant c such that for every n∈ we can decide in time O(n^2(log n)^c) whether two n× n multiplication tables describe isomorphic groups of order  ...  Our complexities are calculated for a deterministic multi-tape Turing machine model. We give the implications to a RAM model in the promise hierarchy as well.  ...  Wilson was supported by a Simons Foundation Grant, identifier #636189. Special thanks to Shyan Akmal for referring us to the work of Rajagopalan-Schulman.  ... 
arXiv:2011.03133v4 fatcat:xkvvwn3dmvgkxodf7jouzrpecm

Page 7442 of Mathematical Reviews Vol. , Issue 97M [page]

1997 Mathematical Reviews  
for Sylow subgroups of small-base permutation groups (257-272); Alice C.  ...  Luks and Akos Seress, Computing the Fitting subgroup and solvable radical of small-base permutation groups in nearly lin- ear time (169-181); David K. Maslen and Daniel N.  ... 

A data structure for a uniform approach to computations with finite groups

Max Neunhöffer, Ákos Seress
2006 Proceedings of the 2006 international symposium on Symbolic and algebraic computation - ISSAC '06  
groups and for Sylow subgroup computations in arbitrary permutation groups.  ...  It provides a framework to process theoretical algorithms which were considered too complicated for implementation such as the asymptotically fastest algorithms for the basic handling of large-base permutation  ...  Experiments show that for permutation degree n > 100, the unified algorithm is about as fast as the nearly lineartime Schreier-Sims algorithm in the case when the input is a small-base group, and it performs  ... 
doi:10.1145/1145768.1145811 dblp:conf/issac/NeunhofferS06 fatcat:yucusqmuufg6lo7x3otkiqe5mq

Pilot Design for Sparse Channel Estimation in Orthogonal Frequency Division Multiplexing Systems

P. Vimala, G. Yamuna
2018 Journal of Telecommunications and Information Technology  
A sufficient condition for the optimal pilot selection from Sylow subgroups is derived. A Sylow subgroup does not exist for most practical OFDM systems.  ...  Therefore, a deterministic pilot search algorithm is described to select pilot locations based on minimizing coherence, along with minimum variance.  ...  Definition for p- Sylow : Sylow Let (G, .) be a group and p be a prime number. If (G) = p a m, where p m, then a subgroup of order p α is called the p-Sylow subgroup of G.  ... 
doi:10.26636/jtit.2018.113817 fatcat:tvq5cnuxrzg7libldvrmackxfy

Construction of Finite Groups

H.U. Besche, B. Eick
1999 Journal of symbolic computation  
The second algorithm can be used to determine the groups of order p n · q with a normal Sylow subgroup for distinct primes p and q.  ...  We introduce three practical algorithms to construct certain finite groups up to isomorphism. The first one can be used to construct all soluble groups of a given order.  ...  Clearly, S is complemented in G by a subgroup K and K has to be a Sylow subgroup for the other prime.  ... 
doi:10.1006/jsco.1998.0258 fatcat:limqcxsqanfrplrnd6rzgo3k44

Computing the soluble radical of a permutation group

W.R. Unger
2006 Journal of Algebra  
Algorithms for computing the soluble radical and p-cores of a permutation group are described.  ...  The algorithms are based on homomorphic reductions, and avoid the computation of Sylow subgroups and the use of backtrack searches.  ...  Acknowledgments The author thanks Charles Leedham-Green for suggesting this approach to computing the soluble radical, Derek Holt for helpful discussions during the algorithm's development,  ... 
doi:10.1016/j.jalgebra.2006.02.027 fatcat:u6xtsmzbdvgvxkmxypjd7wawuu

Computing the character table of a finite group

W.R. Unger
2006 Journal of symbolic computation  
Brauer's theorem on induced characters is an invitation to an algorithm for computing the character table of a finite group.  ...  We report on the performance of the algorithm in computing character tables of various groups, including local subgroups of 3Fi 24 and maximal subgroups of the Monster.  ...  Acknowledgements I would like to thank John Cannon for his enthusiastic support of this project and Eamonn O'Brien for supplying the groups of Fig. 6 .  ... 
doi:10.1016/j.jsc.2006.04.002 fatcat:4yuc72rmivadrov6g6saztjrty

Page 805 of Mathematical Reviews Vol. , Issue 98B [page]

1998 Mathematical Reviews  
In the paper under review the author proves such a logarithmic bound for the class of solvable groups whose Sylow subgroups are all abelian.  ...  A great deal of information about these groups is obtained, and in particular, a nearly complete classification of perfect p’-semiregular groups is given.  ... 

Polynomial-time isomorphism testing of groups of most finite orders [article]

Heiko Dietrich, James B. Wilson
2021 arXiv   pre-print
We prove that for a dense set of positive integers n, isomorphism testing for abelian groups of black-box type of order n can be done in time polynomial in log n.  ...  We also prove that for a dense set of orders n with given prime factors, one can test isomorphism for coprime meta-cyclic groups of black-box type of order n in time polynomial in log n.  ...  Algebra 545 (2020) 174-197. • Group isomorphism is nearly-linear time for most orders.  ... 
arXiv:1806.08872v4 fatcat:vxtl6up2srh45f7juu4gfrn7u4

A recognition algorithm for non-generic classical groups over finite fields

Azice C. Niemeyer, Cheryl E. Praeger
1999 Journal of the Australian Mathematical Society  
linear group.  ...  In a previous paper the authors described an algorithm to determine whether a group of matrices over a finite field, generated by a given set of matrices, contains one of the classical groups or the special  ...  Acknowledgements We are grateful to Tim Penttila, Bob Liebler and Martin Liebeck for helpful advice about the groups of type O + (4, q), O"(4, q) and O + (8, q), respectively.  ... 
doi:10.1017/s1446788700001191 fatcat:g6hfaa5ucjgc3b4a2ldxtxu4ba

A practical model for computation with matrix groups

Henrik Bäärnhielm, Derek Holt, C.R. Leedham-Green, E.A. O'Brien
2015 Journal of symbolic computation  
We describe an algorithm to compute a composition tree for a matrix group defined over a finite field, and show how to use the associated structure to carry out computations with such groups; these include  ...  finding composition and chief series, the soluble radical, and Sylow subgroups.  ...  As outlined in [Ser03, Chapter 6] , an extensive library of highly efficient algorithms exists for small base permutation groups.  ... 
doi:10.1016/j.jsc.2014.08.006 fatcat:5wxh5zfs6fdbleaauqxbbrz6cy
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