in this paper, we extend the construction of a fuzzy subgroup generated by a fuzzy subset to $l$-setting. this construction is illustrated by an example. we also prove that for an $l$-subset of a group, the subgroup generated by its level subset is the level subset of the subgroup generated by that $l$-subset provided the given $l$-subset possesses sup-property.

M. Picantin introduced the notion of Garside groups of spindle type, generalizing the 3-strand braid group. We show that, for linear Garside groups of spindle type, a normal form and a solution to the conjugacy problem are logspace computable. For linear Garside groups of spindle type with homogenous presentation we compute a geodesic normal form in logspace.

Article history: Received 20 January 2012 Available online 26 February 2013 Communicated by Derek Holt

in this paper, we study the notion of solvable $l$-subgroup of an $l$-group and provide its level subset characterization and this justifies the suitability of this extension. throughout this work, we have used normality of an $l$-subgroup of an $l$-group in the sense of wu rather than liu.

In this paper, we extend the construction of a fuzzy subgroup generated by a fuzzy subset to $L$-setting. This construction is illustrated by an example. We also prove that for an $L$-subset of a group, the subgroup generated by its level subset is the level subset of the subgroup generated by that $L$-subset provided the given $L$-subset possesses sup-property.

We consider the class of finitely generated groups which have a normal form computable in logspace. We prove that the class of such groups is closed under passing to finite index subgroups, direct products, wreath products, and certain free products and infinite extensions, and includes the solvable Baumslag-Solitar groups, as well as non-residually finite (and hence nonlinear) examples. We def...

In the present paper we investigate a special class of two-dimensional rational surfaces Φ in R whose tangent planes satisfy the following property: For any threespace E in R there exists a unique tangent plane T (u, v) of Φ which is parallel to E. For all possible varieties of tangent planes T (u, v) the corresponding families of surfaces in R are constructed explicitly. Quadratic triangular B...

We present almost complete list of normal forms of classical r-matrices on the Poincaré group.

For finitely generated nilpotent groups, we employ Mal’cev coordinates to solve several classical algorithmic problems efficiently. Computation of normal forms, the membership problem, the conjugacy problem, and computation of presentations for subgroups are solved using only logarithmic space and, simultaneously, in quasilinear time. Compressed-word versions of these problems, in which each in...

The zero bias distribution W ∗ of W , defined though the characterizing equation EWf(W ) = σ2Ef ′(W ∗) for all smooth functions f , exists for all W with mean zero and finite variance σ2. For W and W ∗ defined on the same probability space, the L1 distance between F , the distribution function of W with EW = 0 and Var(W ) = 1, and the cumulative standard normal Φ has the simple upper bound ||F ...