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

2021
*
arXiv
*
pre-print

We show that there is

arXiv:2011.03133v4
fatcat:xkvvwn3dmvgkxodf7jouzrpecm
*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. ...##
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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. ...

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

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 ...

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

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. ...

##
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Construction of Finite Groups

1999
*
Journal of symbolic computation
*

The second

doi:10.1006/jsco.1998.0258
fatcat:limqcxsqanfrplrnd6rzgo3k44
*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. ...##
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Computing the soluble radical of a permutation group

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, ...

##
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Computing the character table of a finite group

2006
*
Journal of symbolic computation
*

Brauer's theorem on induced characters is an invitation to an

doi:10.1016/j.jsc.2006.04.002
fatcat:4yuc72rmivadrov6g6saztjrty
*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 . ...##
###
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. ...

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

2021
*
arXiv
*
pre-print

We prove that

arXiv:1806.08872v4
fatcat:vxtl6up2srh45f7juu4gfrn7u4
*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. ...##
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A recognition algorithm for non-generic classical groups over finite fields

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. ...

##
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A practical model for computation with matrix groups

2015
*
Journal of symbolic computation
*

We describe an

doi:10.1016/j.jsc.2014.08.006
fatcat:5wxh5zfs6fdbleaauqxbbrz6cy
*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*. ...
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