862 research outputs found
The Kervaire-Laudenbach conjecture and presentations of simple groups
The statement ``no nonabelian simple group can be obtained from a nonsimple
group by adding one generator and one relator"
1) is equivalent to the Kervaire--Laudenbach conjecture;
2) becomes true under the additional assumption that the initial nonsimple
group is either finite or torsion-free.
Key words: Kervaire--Laudenbach conjecture, relative presentations, simple
groups, car motion, cocar comotion.
AMS MSC: 20E32, 20F05, 20F06.Comment: 20 pages, 13 figure
Easy Monitored Entangled States
We discuss the generation and monitoring of durable atomic entangled state
via Raman-type process, which can be used in the quantum information
processing.Comment: 9 pages, 2 figures, the previous title "Durable Entanglement in
Atomic Systems" is replaced by new title, accepted to Appl. Phys. Let
Economical adjunction of square roots to groups
How large must an overgroup of a given group be in order to contain a square
root of any element of the initial group? We give an almost exact answer to
this question (the obtained estimate is at most twice worse than the best
possible) and state several related open questions.Comment: 5 pages. A Russian version of this paper is at
http://mech.math.msu.su/department/algebra/staff/klyachko/papers.htm V2:
minor correction
Free subgroups of one-relator relative presentations
Suppose that G is a nontrivial torsion-free group and w is a word over the
alphabet G\cup\{x_1^{\pm1},...,x_n^{\pm1}\}. It is proved that for n\ge2 the
group \~G= always contains a nonabelian free subgroup.
For n=1 the question about the existence of nonabelian free subgroups in \~G is
answered completely in the unimodular case (i.e., when the exponent sum of x_1
in w is one). Some generalisations of these results are discussed.Comment: V3: A small correction in the last phrase of the proof of Theorem 1.
4 page
Connecting N-representability to Weyl's problem: The one particle density matrix for N = 3 and R = 6
An analytic proof is given of the necessity of the Borland-Dennis conditions
for 3-representability of a one particle density matrix with rank 6. This may
shed some light on Klyachko's recent use of Schubert calculus to find general
conditions for N-representability
- …