共查询到20条相似文献,搜索用时 109 毫秒
1.
Let p be a prime, G
a finite group which has a normal p-subgroup
containing its own centralizer in G, and
R a commutative local ring with residue class
field of characteristic p. In this paper, it is
shown that if
is an augmented automorphism of
RG which fixes a Sylow
p-subgroup P
of G, there is
such that
for all
and
is an inner automorphism of
RG.
Received: 26 July 2000 相似文献
2.
Let KGbe the group algebra of a p1 -group Gover a field Kof characteristic p > 0, and let U(KG)be its group of units. If KGcontains a nontrivial bicyclic unit and if Kis not algebraic over its prime field, then we prove that the free product Zp? Zp? Zpcan be embedded in U(KG). 相似文献
3.
A representation
G
U(n)
of degree n has
fixity equal to the smallest integer
f such that the induced action
of G on
U(n)
/U(n-f-1)
is free. Using bundle theory we show that if G
admits a representation of fixity one, then it acts freely and smoothly on
We use this to prove that a finite
p-group (for
p > 3)
acts freely and smoothly on a product of two spheres if and only if it does not
contain ( /p)3
as a subgroup.
We use propagation methods from surgery theory
to show that a representation of fixity
f <
n - 1 gives rise to a free
action of G
on a product of f + 1
spheres provided the order of G
is relatively prime to (n - 1)!.
We give an infinite collection of new examples of finite
p-groups of rank
r which act freely on a product of
r spheres, hence verifying a strong
form of a well-known conjecture for these groups. In addition we show that
groups of fixity two act freely on a finite complex
with the homotopy type of a product of three spheres. A number of
examples are explicitly described. 相似文献
4.
Gérard Endimioni 《Monatshefte für Mathematik》2009,156(1):23-29
Let G be a group and let n be a positive integer. A polynomial function in G is a function from G
n
to G of the form , where f(x
1, . . . , x
n
) is an element of the free product of G and the free group of rank n freely generated by x
1, . . . , x
n
. There is a natural definition for the product of two polynomial functions; equipped with this operation, the set of polynomial functions is a group. We prove that this group is polycyclic if and only if G is finitely generated, soluble, and nilpotent-by-finite. In particular, if the group of polynomial functions is polycyclic,
then necessarily it is nilpotent-by-finite. Furthermore, we prove that G itself is polycyclic if and only if the subgroup of polynomial functions which send (1, . . . , 1) to 1 is finitely generated
and soluble.
相似文献
5.
Robert L. Griess Jr 《Geometriae Dedicata》1991,39(3):253-305
Let
be an algebraically closed field and let G be a finite-dimensional algebraic group over
which is nearly simple, i.e. the connected component of the identity G
0 is perfect, C
G(G
0)=Z(G
0) and G
0/Z(G
0) is simple. We classify maximal elementary abelian p-subgroups of G which consist of semisimple elements, i.e. for all primes p char
.Call a group quasisimple if it is perfect and is simple modulo the center. Call a subset of an algebraic group toral if it is in a torus; otherwise nontoral. For several quasisimple algebraic groups and p=2, we define complexity, and give local criteria for whether an elementary abelian 2-subgroup of G is toral.For all primes, we analyze the nontoral examples, include a classification of all the maximal elementary abelian p-groups, many of the nonmaximal ones, discuss their normalizers and fusion (i.e. how conjugacy classes of the ambient algebraic group meet the subgroup). For some cases, we give a very detailed discussion, e.g. p=3 and G of type E
6, E
7 and E
8. We explain how the presence of spin up and spin down elements influences the structure of projectively elementary abelian 2-groups in Spin(2n, ). Examples of an elementary abelian group which is nontoral in one algebraic group but toral in a larger one are noted.Two subsets of a maximal torus are conjugate in G iff they are conjugate in the normalizer of the torus; this observation, with our discussion of the nontoral cases, gives a detailed guide to the possibilities for the embedding of an elementary abelian p-group in G. To give an application of our methods, we study extraspecial p-groups in E
8(
).Dedicated to Jacques Tits for his sixtieth birthday 相似文献
6.
Let G be a locally
-proper group, S Syl5(G), and Z = Z(S). We demonstrate that if
is 5-constrained and Z is not weakly closed in O5(NG (Z)) then G is isomorphic to the monster sporadic simple group.Received: 2 October 2003 相似文献
7.
For every open subset G of
and for every continuous, strictly positive weight v on G, the Banach space
of all the holomorphic functions f on
G such that
vanishes at infinity on G, endowed with the natural weighted
sup-norm, is isomorphic to a closed subspace of the Banach
space c0; hence it is reflexive if and only if it is finite
dimensional.Received: 30 September 2002 相似文献
8.
9.
Let
be the Hecke algebra of the symmetric group
over a field K of characteristic
and
a primitive
-th root of one in K. We show that an
-module is projective if and only if its restrictions to any
-parabolic subalgebra of
is projective.
Moreover, we give a new construction of blocks of
-parabolic subalgebras, in terms of skew group algebras over local commutative
algebras.
Received: 30 June 2003 相似文献
10.
Bernhard Schmidt 《Journal of Algebraic Combinatorics》1997,6(3):279-297
This paper provides new exponent and rank conditions for the existence of abelian relative (p
a,p
b,p
a,p
a–b)-difference sets. It is also shown that no splitting relative (22c,2d,22c,22c–d)-difference set exists if d > c and the forbidden subgroup is abelian. Furthermore, abelian relative (16, 4, 16, 4)-difference sets are studied in detail; in particular, it is shown that a relative (16, 4, 16, 4)-difference set in an abelian group G Z8 × Z4 × Z2 exists if and only if exp(G) 4 or G = Z8 × (Z2)3 with N Z2 × Z2. 相似文献
11.
It is well known that a permutation group of degree
can be generated by
elements. In this paper we study
the asymptotic behavior of the probability of generating a
permutation group of degree n with
elements. In particular we prove that if n
is large enough and
elements generate a permutation group
G of degree
n
modulo G
G
2, then almost
certainly these elements generate G itself.
Received: 2 January 2002 相似文献
12.
An n-subsetD of a group G of order
is called an affine difference set of G relativeto a normal subgroup N of G of order
if the list of differences
containseach element of G-N exactly once and no elementof N. It is a well-known conjecture that if Dis an affine difference set in an abelian group G,then for every prime p, the Sylow p-subgroupof G is cyclic. In Arasu and Pott [1], it was shownthat the above conjecture is true when
. In thispaper we give some conditions under which the Sylow p-subgroupof G is cyclic. 相似文献
13.
Letk be any field andG a finite group. Given a cohomology class α∈H
2(G,k
*), whereG acts trivially onk
*, one constructs the twisted group algebrak
αG. Unlike the group algebrakG, the twisted group algebra may be a division algebra (e.g. symbol algebras, whereG⋞Z
n×Zn). This paper has two main results: First we prove that ifD=k
α
G is a division algebra central overk (equivalentyD has a projectivek-basis) thenG is nilpotent andG’ the commutator subgroup ofG, is cyclic. Next we show that unless char(k)=0 and
, the division algebraD=k
α
G is a product of cyclic algebras. Furthermore, ifD
p is ap-primary factor ofD, thenD
p is a product of cyclic algebras where all but possibly one are symbol algebras. If char(k)=0 and
, the same result holds forD
p, p odd. Ifp=2 we show thatD
2 is a product of quaternion algebras with (possibly) a crossed product algebra (L/k,β), Gal(L/k)⋞Z
2×Z2n. 相似文献
14.
Mehdi Shabani Attar 《Archiv der Mathematik》2007,89(4):296-297
Let G be a group and let Aut
c
(G) be the group of central automorphisms of G. Let
be the set of all central automorphisms of G fixing Z(G) elementwise. In this paper we prove that if G is a finite p-group, then
= Inn(G) if and only if G is abelian or G is nilpotent of class 2 and Z(G) is cyclic.
This work was supported in part by the Center of Excellence for Mathematics, University of Isfahan, Iran.
Received: 30 October 2006 相似文献
15.
Let G be a finite group,
a normal subgroup, p a prime,
a finite splitting field of characteristic p for
G and
We prove that
is a splitting field for N, using the action
of the Galois group of the field extension
on the irreducible representations of N.
As
is a splitting field for the symmetric group
Sn
we get as a corollary that
is a splitting field for the alternating group
An.
Received: 31 July 2003 相似文献
16.
18.
19.
20.
Dr. Eugene Spiegel 《Monatshefte für Mathematik》1976,81(4):305-309
SupposeP is the ring ofp-adic integers,G is a finite group of orderp
n
, andPG is the group ring ofG overP. IfV
p
(G) denotes the elements ofPG with coefficient sum one which are of order a power ofp, it is shown that the elements of any subgroupH ofV
p
(G) are linearly independent overP, and if in additionH is of orderp
n
, thenPGPH. As a consequence, the lattice of normal subgroups ofG and the abelianization of the normal subgroups ofG are determined byPG. 相似文献