971 research outputs found
On permutizers of subgroups of finite groups
Finite groups with given systems of permuteral and strongly permuteral
subgroups are studied. New characterizations of w-supersoluble and supersoluble
groups are received.Comment: 11 page
Arithmetic graphs of finite groups
In this paper we introduced an arithmetic graph function which associates
with every group G the directed graph whose vertices corresponds to the
divisors of |G|. With the help of such functions we introduced arithmetic
graphs of classes of groups, in particular of hereditary saturated formations.
We formulated the problem of the recognition of classes of groups by arithmetic
graph functions and investigated this problem for some arithmetic graph
functions
On partially conjugate-permutable subgroups of finite groups
Let be a subset of a group . We call a subgroup of the
-conjugate-permutable subgroup of , if for all .
This concept is a generalization of conjugate-permutable subgroups introduced
by T. Foguel. Our work focuses on the influence of -conjugate-permutable
subgroups on the structure of finite groups in case when is the Fitting
subgroup or its generalizations (introduced by H. Bender in 1970)
and (introduced by P. Shmid 1972). We obtain a new criteria for
nilpotency and supersolubility of finite groups which generalize some well
known results
The graph of atomic divisors and constructive recognition of finite simple groups
The spectrum of a finite group is the set of orders of
elements of . We present a polynomial-time algorithm that, given a finite
set of positive integers, outputs either an empty set or a finite
simple group . In the former case, there is no finite simple group with
, while in the latter case,
and for all finite
simple groups with
On the structure of finite groups isospectral to finite simple groups
Finite groups are said to be isospectral if they have the same sets of
element orders. A finite nonabelian simple group is said to be almost
recognizable by spectrum if every finite group isospectral to is an almost
simple group with socle isomorphic to . It is known that all finite simple
sporadic, alternating and exceptional groups of Lie type, except , ,
and , are almost recognizable by spectrum. The present paper
is the final step in the proof of the following conjecture due to V.D. Mazurov:
there exists a positive integer such that every finite simple classical
group of dimension larger than is almost recognizable by spectrum.
Namely, we prove that a nonabelian composition factor of a~finite group
isospectral to a finite simple symplectic or orthogonal group of dimension
at least 10, is either isomorphic to or not a group of Lie type in the same
characteristic as , and combining this result with earlier work, we deduce
that Mazurov's conjecture holds with .Comment: 13 page
Generalized Fitting subgroups of finite groups
In this paper we consider the Fitting subgroup of a finite group
and its generalizations: the quasinilpotent radical and the
generalized Fitting subgroup defined by and . We sum up known properties
of and suggest some new ones. Let be a subgroup of a group
. We shall call a subgroup of the -subnormal subgroup if is
subnormal in . In this work the influence of -subnormal
subgroups (maximal, Sylow, cyclic primary) on the structure of finite groups
are studied in the case when
Renormalization group, operator product expansion and anomalous scaling in models of passive turbulent advection
The field theoretic renormalization group is applied to Kraichnan's model of
a passive scalar quantity advected by the Gaussian velocity field with the pair
correlation function . Inertial-range
anomalous scaling for the structure functions and various pair correlators is
established as a consequence of the existence in the corresponding operator
product expansions of ``dangerous'' composite operators (powers of the local
dissipation rate), whose {\it negative} critical dimensions determine anomalous
exponents. The latter are calculated to order of the
expansion (three-loop approximation).Comment: 4 page
Renormalization group in the statistical theory of turbulence: Two-loop approximation
The field theoretic renormalization group is applied to the stochastic
Navier--Stokes equation that describes fully developed fluid turbulence. The
complete two-loop calculation of the renormalization constant, the beta
function and the fixed point is performed. The ultraviolet correction exponent,
the Kolmogorov constant and the inertial-range skewness factor are derived to
second order of the expansion.Comment: 5 page
Shape memory ferromagnets
In ferromagnetic alloys with shape memory large reversible strains can be
obtained by rearranging the martensitic domain structure by a magnetic field.
Magnetization through displacement of domain walls is possible in the presence
of high magnetocrystalline anisotropy, when martensitic structure rearrangement
is energetically favorable compared to the reorientation of magnetic moments.
In ferromagnetic Heusler alloys NiMnGa the Curie temperature
exceeds the martensitic transformation temperature. The fact that these two
temperatures are close to room temperature offers the possibility of
magnetically controlling the shape and size of ferromagnets in the martensitic
state. In NiMnGa single crystals, a reversible strain of % is obtained in fields of T.Comment: review on ferromagnetic shape memory alloys (FSMAs
On Order-Disorder () Phase Transition in NiGa Heusler Alloys
Order-disorder phase transition in NiGa Heusler alloys has
been studied. It was found that the phase transition in
Ni2+xMn1-xGa (x = 0.16 - 0.20) Heusler alloys is of second order and the
temperature of this transition decreases with Ni excess.Comment: 3 pages, 3 figures, revtex
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