a gyrogroup is a nonassociative group-like structure modelled on the space of relativistically admissible velocities with a binary operation given by einstein's velocity addition law. in this article, we present a few of groups sitting inside a gyrogroup $g$, including the commutator subgyrogroup, the left nucleus, and the radical of $g$. the normal closure of the commutator subgyrogroup, ...

This paper proposes a low power commutator architecture based on triple port RAMs rather than dual port RAMs or conventional FIFO.for the radix-4 pipelined FFT processor implementation. The triple port RAM based commutator consumes less power than the other two for the first and second stages of a 64-point radix-4 pipelined FFT processor. This commutator is attractive for shorter FFT’s but can ...

In this paper, a good λ estimate for the multilinear commutator associated to the fractional integral operator on the spaces of homogeneous type is obtained. Under this result, we get the(Lp(X),Lq(X)) -boundedness of the multilinear commutator. Mathematics subject classification (2010): 42B20, 42B25.

It is shown that there exists a finitely generated infinite simple group of infinite commutator width, and that the commutator width of a finitely generated infinite boundedly simple group can be arbitrarily large. Besides, such groups can be constructed with decidable word and conjugacy problems.

In this paper, we prove the sharp function inequality for the multilinear commutator related to the singular integral operator with variable Calderón-Zygmund kernel. By using the sharp inequality, we obtain the Lnorm inequality for the multilinear commutator. 2000 Mathematics Subject Classification: 42B20, 42B25.

In this paper we consider the vector-valued extension of the Fefferman-Stein-Stronberg sharp maximal inequality under growth condition. As an application we obtain the vectorvalued extension of the boundedness of the commutator. Furthermore we prove the boundedness of the commutator.

We show that strongly protomodular categories (as the category Gp of groups for instance) provide an appropriate framework in which the commutator of two equivalence relations do coincide with the commutator of their associated normal subobjects, whereas it is not the case in any semi-abelian category.

Henriques and Kamnitzer defined a commutator in the category of crystals for complex semisimple Lie algebras based on Lusztig’s involution on a crystal. More recently, Kamnitzer and Tingley proved that the action of this commutator on the highest weight elements (which determines it) is given by Kashiwara’s involution on the Verma crystal. Both of these definitions depend on some maps of crysta...

In the paper we consider some commutator-type and power-type matrix equations in the group UT(∞,K) of infinite dimensional unitriangular matrices over a fieldK. We introduce a notion of a power outer commutator ω1k k (x1, ..., xk) and a power Engel commutator e1k k (x, y) as outer (respectively Engel) commutators modified by allowing powers of letters instead of letters alone. For a given infin...