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Displaying similar documents to “Soluble products of connected subgroups.”

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.

Some questions on quasinilpotent groups and related classes.

M.J. Iranzo, J. Medina, F. Pérez-Monasor (2002)

Revista Matemática Iberoamericana

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In this paper we will prove that if G is a finite group, X a subnormal subgroup of X F*(G) such that X F*(G) is quasinilpotent and Y is a quasinilpotent subgroup of NG(X), then Y F*(NG(X)) is quasinilpotent if and only if Y F*(G) is quasinilpotent. Also we will obtain that F*(G) controls its own fusion in G if and only if G = F*(G).

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. ...