Displaying similar documents to “On minimal non-supersoluble groups.”

Computation of centralizers in Braid groups and Garside groups.

Nuno Franco, Juan González-Meneses (2003)

Revista Matemática Iberoamericana

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We give a new method to compute the centralizer of an element in Artin braid groups and, more generally, in Garside groups. This method, together with the solution of the conjugacy problem given by the authors in [9], are two main steps for solving conjugacy systems, thus breaking recently discovered cryptosystems based in braid groups [2]. We also present the result of our computations, where we notice that our algorithm yields surprisingly small generating sets for the centralizers. ...

A computer algebra solution to a problem in finite groups.

Gert-Martin Greuel (2003)

Revista Matemática Iberoamericana

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We report on a partial solution of the conjecture that the class of finite solvable groups can be characterised by 2-variable identities. The proof requires pieces from number theory, algebraic geometry, singularity theory and computer algebra. The computations were carried out using the computer algebra system SINGULAR.

On some permutable products of supersoluble groups.

Manuel J. Alejandre, A. Ballester-Bolinches, John Cossey, M. C. Pedraza-Aguilera (2004)

Revista Matemática Iberoamericana

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It is well known that a group G = AB which is the product of two supersoluble subgroups A and B is not supersoluble in general. Under suitable permutability conditions on A and B, we show that for any minimal normal subgroup N both AN and BN are supersoluble. We then exploit this to establish some sufficient conditions for G to be supersoluble.

A note on lifting of Carnot groups.

Andrea Bonfiglioli, Francesco Uguzzoni (2005)

Revista Matemática Iberoamericana

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We prove that every homogeneous Carnot group can be lifted to a free homogeneous Carnot group. Though following the ideas of Rothschild and Stein, we give simple and self-contained arguments, providing a constructive proof, as shown in the examples.