Communications in Algebra

Komissartschik, Edward A.; Tsaranov, Sergey V.

doi: 10.1080/00927878608823389pmid: N/A

This paper contains a list of intersections of all pairs of maximal subgroups in nonabelian simple groups of order less than 106 excluding PSL(2,q3 for q > 9. To compute possible orders of intersections a computer was used.

Bruyn, Lieven Le

doi: 10.1080/00927878608823390pmid: N/A

Bruyn, L.Le ; Bergh, M.Van der; Oystaeyen, F.Van

doi: 10.1080/00927878608823391pmid: N/A

Mitsuda, Tadashi

doi: 10.1080/00927878608823392pmid: N/A

Babai, László

doi: 10.1080/00927878608823393pmid: N/A

We prove that for n≥2, the length of every subgroup chain in Sn is at most 2n-3. The proof rests on an upper bound for the order of primitive permutation groups, due to Praeger and Saxl. The result has applications to worst case complexity estimates for permutation group algorithms.

Van Casteren, Jan A.

doi: 10.1080/00927878608823394pmid: N/A

Let X and Y be complex analytic manifolds of the same complex dimension, let p be a point in T * X\{0} and let q be a point in T * Y\{0}. Let ϵ (p) (resp. ϵ (q)) denote the graded ring of germs of micro-differential operators at p (resp. q). Supply ϵ (p) and ϵ (q) with a suitable and natural convergence structure. Let X: ϵ (p) ϵ → (q) be a continuous degree preserving ring isomorphism. We show that there exists a vector field ∂ tangent to X in a neighbourhood of л(q), a symplectic map ф defined on a conic open neighbourhood of q to a similar neighbourhood of p such that for an appropriate constant z and a suitable invertible element A. in ϵ (q) of degree 0. Uniqueness of this result is discussed and a global version is also given. Here < ∂, ξ > denotes the duality between T(Y) and T *(Y). of do,(X) = 1, then this representation is canonical.

narang, Kamal

doi: 10.1080/00927878608823395pmid: N/A

Smith, Kirby C.

doi: 10.1080/00927878608823396pmid: N/A