405 research outputs found
On the number of classes of conjugate Hall subgroups in finite simple groups
In this paper we find the number of conjugate -Hall subgroups in all
finite almost simple groups. We also complete the classification of -Hall
subgroups in finite simple groups and correct some mistakes from our previous
paper.Comment: article in press in "Journal of algebra
Existence criterion for Hall subgroups of finite groups
In the paper we obtain an existence criterion for Hall subgroups of finite
groups in terms of a composition series.Comment: We made some editor corrections in the tex
Classification and properties of the -submaximal subgroups in minimal nonsolvable groups
Let be a set of primes. According to H. Wielandt, a subgroup of a
finite group is called a -submaximal subgroup if there is a
monomorphism into a finite group such that
is subnormal in and for a -maximal subgroup
of . In his talk at the well-known conference on finite groups in Santa-Cruz
(USA) in 1979, Wielandt posed a series of open questions and among them the
following problem: to describe the -submaximal subgroup of the minimal
nonsolvable groups and to study properties of such subgroups: the pronormality,
the intravariancy, the conjugacy in the automorphism group etc. In the article,
for every set of primes, we obtain a description of the -submaximal
subgroup in minimal nonsolvable groups and investigate their properties, so we
give a solution of Wielandt's problem
Fine tuning of phase qubit parameters for optimization of fast single-pulse readout
We analyze a two-level quantum system, describing the phase qubit, during a
single-pulse readout process by a numerical solution of the time-dependent
Schroedinger equation. It has been demonstrated that the readout error has a
minimum for certain values of the system`s basic parameters. In particular, the
optimization of the qubit capacitance and the readout pulse shape leads to
significant reduction of the readout error. It is shown that in an ideal case
the fidelity can be increased to almost 97% for 2 ns pulse duration and to 96%
for 1 ns pulse duration.Comment: 4 pages, 5 figure
Groups with bounded centralizer chains and the~Borovik--Khukhro conjecture
Let be a locally finite group and the Hirsch--Plotkin radical of
. Denote by the full inverse image of the generalized Fitting subgroup
of in . Assume that there is a number such that the length of
every chain of nested centralizers in does not exceed . The
Borovik--Khukhro conjecture states, in particular, that under this assumption
the quotient contains an abelian subgroup of index bounded in terms of
. We disprove this statement and prove some its weaker analog
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