1,144 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
-Closure of -transitive group in polynomial time
Let be a permutation group on a finite set . The -closure
of the group is the largest subgroup of
having the same orbits as on the -th
Cartesian power of . A group is called
-transitive if its transitive and the orbits of a point stabilizer
on the set are of the same size greater
than one. We prove that the -closure of a -transitive
permutation group can be found in polynomial time in size of . In
addition, if the group is not -transitive, then for every positive
integer its -closure can be found within the same time. Applying the
result, we prove the existence of a polynomial-time algorithm for solving the
isomorphism problem for schurian -homogeneous coherent
configurations, that is the configurations naturally associated with
-transitive groups
Locally finite groups with bounded centralizer chains
The c-dimension of a group G is the maximal length of a chain of nested
centralizers in G. We prove that a locally finite group of finite c-dimension k
has less than 5k nonabelian composition factors.Comment: 4 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
Almost recognizability by spectrum of simple exceptional groups of Lie type
The spectrum of a finite group is the set of its elements orders. Groups are
said to be isospectral if their spectra coincide. For every finite simple
exceptional group , we prove that each finite group isospectral to
is isomorphic to a group squeezed between and its automorphism
group, that is ; in particular, up-to
isomorphism, there are only finitely many such groups. This assertion, together
with a series of previously obtained results, implies that the same is true for
every finite simple exceptional group except the group .Comment: minor changes, Tables 2 and 3 are fixe
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
Condensation of electron-hole pairs in a degenerate semiconductor at room temperature
It has been theoretically shown that in large-density semiconductor plasma
there exist an energy level of a bound electron-hole pair (a composite boson)
at the band gap. Filling this level up occurs through the condensation of
electron-hole pairs with the use of mediating photons of a resonant
electromagnetic field. We have demonstrated that in the case of a strong
degeneracy of the plasma the critical temperature of the condensation is
determined by the Fermi energies of the plasma components rather than the order
parameter D. The critical temperature can exceed 300 K at electron-hole
densities as large as 6.1018 cm-3. The theoretical model is consistent with
available experimental dataComment: 26 pages, 5 figures Submitted to Physical Review
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
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
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
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