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1.
W. O. Alltop 《Israel Journal of Mathematics》1976,23(1):31-38
ItH
i
is a finite non-abelianp-group with center of orderp, for 1≦j≦R, then the direct product of theH
i
does not occur as a normal subgroup contained in the Frattini subgroup of any finitep-group. If the Frattini subgroup Φ of a finitep-groupG is cyclic or elementary abelian of orderp
2, then the centralizer of Φ inG properly contains Φ. Non-embeddability properties of products of groups of order 16 are established. 相似文献
2.
LetG be a finitep-group, and letU(G) be the group of units of the group algebraFG, whereF is a field of characteristicp. It is shown that, if the commutative subgroup ofG has order at leastp
2, then the nilpotency class ofU(G) is at least 2p−1.
The authors are grateful to the Dipartimento di Matematica of the Universita di Trento, and to the Mathematical Institute
of the University of Oxford, for their hospitality while this paper was being written. Then are also grateful to Robert Sandling,
for communication of results, and problems, prior to publication. 相似文献
3.
Thomas Meixner 《Israel Journal of Mathematics》1981,38(4):345-360
For a finite groupG letA(G) denote the group of power automorphisms, i.e. automorphisms normalizing every subgroup ofG. IfG is ap-group of class at mostp, the structure ofA (G) is shown to be rather restricted, generalizing a result of Cooper ([2]). The existence of nontrivial power automorphisms,
however, seems to impose restrictions on thep-groupG itself. It is proved that the nilpotence class of a metabelianp-group of exponentp
2 possessing a nontrival power automorphism is bounded by a function ofp. The “nicer” the automorphism—the lower the bound for the class. Therefore a “type” for power automorphisms is introduced.
Several examples ofp-groups having large power automorphism groups are given. 相似文献
4.
A. Laradji 《Archiv der Mathematik》2002,79(6):418-422
Let π be a set of prime numbers andG a finite π-separable group. Let θ be an irreducible π′-partial character of a normal subgroupN ofG and denote by Iπ′ (G‖θ), the set of all irreducible π′-partial characters Φ ofG such that θ is a constituent of ΦN. In this paper, we obtain some information about the vertices of the elements in Iπ′ (G‖θ). As a consequence, we establish an analogue of Fong's theorem on defect groups of covering blocks, for the vertices of
the simple modules (in characteristicsp) of a finitep-solvable group lying over a fixed simple module of a normal subgroup. 相似文献
5.
SupposeG is a finitep-group andk is the field ofp elements, and letU be the augmentation ideal of the group algebrakG. We investigate whichp-groups,G, have normal complements in their modp-envelope,G
*.G
* is defined byG
*={1−u∶u∈U}. 相似文献
6.
A division ring D is said to be weakly locally finite if for every finite subset ${S \subset D}$ , the division subring of D generated by S is centrally finite. It is known that the class of weakly locally finite division rings strictly contains the class of locally finite division rings. In this note we prove that every non-central subnormal subgroup of the multiplicative group of a weakly locally finite division ring contains a non-cyclic free subgroup. This generalizes the previous result by Gonçalves for centrally finite division rings. 相似文献
7.
Kai Xu 《Israel Journal of Mathematics》1996,93(1):189-194
LetX be a finitep-torsion based connected nilpotent CW-complex. We give a criterion of a subgroup of ε(X), the group of self equivalences ofX, to be a nilpotent group, in terms of its action onE
*(X), whereE is a CW-spectrum, satisfying some technical conditions. 相似文献
8.
If π is a set of primes, a finite group G is block π-separated if for every two distinct irreducible complex characters α, β ∈ Irr(G) there exists a prime p ∈ π such that α and β lie in different Brauer p-blocks. A group G is block separated if it is separated by the set of prime divisors of |G|. Given a set π with n different primes, we construct an example of a solvable π-group G which is block separated but it is not separated by every proper subset of π.
Received: 22 December 2004 相似文献
9.
D. N. Azarov 《Russian Mathematics (Iz VUZ)》2017,61(5):1-6
Let p be a prime number. Recall that a group G is said to be a residually finite p-group if for every non-identity element a of G there exists a homomorphism of the group G onto a finite p-group such that the image of a does not coincide with the identity. We obtain a necessary and sufficient condition for the free product of two residually finite p-groups with finite amalgamated subgroup to be a residually finite p-group. This result is a generalization of Higman’s theorem on the free product of two finite p-groups with amalgamated subgroup. 相似文献
10.
Zu Yun Lu 《数学学报(英文版)》2002,18(2):335-338
Let N be a normal subgroup of a finite group G. Let ϕ be an irreducible Brauer character of N. Assume π is a set of primes and χ(1)/ϕ(1) is a π′-number of any χ∈IBr
p
(G/ϕ). If p∤|G:N|, and N is p-solvable, then G/N has an abelian-by-metabelian Hall-π subgroup; If p∉π then G/N has a metabelian Hall-π subgroup.
Received February 22, 2000, Accepted May 9, 2001 相似文献
11.
W. Mack Hill 《Israel Journal of Mathematics》1974,19(3):208-211
A nonabelianp-group with cyclic center cannot occur as a normal subgroup contained in the Frattini subgroup of ap-closed group. If a nonabelian normal subgroup of orderp
n
and nilpotence classk is contained in the Frattini subgroup of ap-closed group, then its exponent is a divisor ofp
n−k
. This fact is used to derive a relation among the order, number of generators, exponent, and class of the Frattini subgroup,
forp-groups. Finally, it is conjectured that a nonabelianp-group having center of orderp cannot occur as a normal subgroup contained in the Frattini subgroup of any finite group. A proof is given forp-supersolvable groups. 相似文献
12.
Burkhard Külshammer 《Israel Journal of Mathematics》1995,92(1-3):295-306
Donovan’s conjecture, on blocks of finite group algebras over an algebraically closed field of prime characteristicp, asserts that for any finitep-groupD, there are only finitely many Morita equivalence classes of blocks with defect groupD. The main result of this paper is a reduction theorem: It suffices to prove the conjecture for groups generated by conjugates
ofD. A number of other finiteness results are proved along the way. The main tool is a result on actions of algebraic groups. 相似文献
13.
Leila Schneps 《Israel Journal of Mathematics》1996,93(1):125-144
LetG be a finite group of even order, having a central element of order 2 which we denote by −1. IfG is a 2-group, letG be a maximal subgroup ofG containing −1, otherwise letG be a 2-Sylow subgroup ofG. LetH=G/{±1} andH=G/{±1}. Suppose there exists a regular extensionL
1 of ℚ(T) with Galois groupG. LetL be the subfield ofL
1 fixed byH. We make the hypothesis thatL
1 admits a quadratic extensionL
2 which is Galois overL of Galois groupG. IfG is not a 2-group we show thatL
1 then admits a quadratic extension which is Galois over ℚ(T) of Galois groupG and which can be given explicitly in terms ofL
2. IfG is a 2-group, we show that there exists an element α ε ℚ(T) such thatL
1 admits a quadratic extension which is Galois over ℚ(T) of Galois groupG if and only if the cyclic algebra (L/ℚ(T).a) splits. As an application of these results we explicitly construct several 2-groups as Galois groups of regular extensions
of ℚ(T). 相似文献
14.
B. A. F. Wehrfritz 《Monatshefte für Mathematik》2000,49(5):153-157
Let V be a left vector space over a division ring D and the group of all D-automorphisms of V. A subgroup G of is completely reducible of V is completely reducible as D–G bimodule. Our aim in this brief note is to point out that in a sense the very useful notion of a local marker extends from V finite-dimensional to V infinite-dimensional. (A local marker of a subgroup G of is any finitely generated subgroup X of G such that row n-space has least composition length as D–X bimodule. A local marker of G controls to a considerable extent the local behaviour of G.) Our main result is the following. Let G be a completely reducible subgroup of and let W be any finite-dimensional D-subspace of V. Then G has a finitely generated subgroup X such that for every finitely generated subgroup Y of G containing X the D–Y submodule WY has a D–Y submodule M with and completely reducible. We also give some examples and state without proof some stronger conclusions valid for various special subgroup G. 相似文献
15.
Sándor Szabó 《Aequationes Mathematicae》1989,38(2-3):186-191
Summary If a finite abelian (p, q)-group whosep-Sylow subgroup is cyclic is factorized by subsets of cardinalitiesq or a power ofp, then at least one of the factors is periodic. 相似文献
16.
J. W. Wamsley 《Israel Journal of Mathematics》1972,11(3):297-298
LetG be a finitep-group,d(G)=dimH
1 (G, Z
p) andr(G)=dimH
2(G, Zp). Thend(G) is the minimal number of generators ofG, and we say thatG is a member of a classG
p
of finitep-groups ifG has a presentation withd(G) generators andr(G) relations. We show that ifG is any finitep-group, thenG is the direct factor of a member ofG
p
by a member ofG
p
. 相似文献
17.
LetX
1 andX
2 be two mixing Markov shifts over finite alphabet. If the entropy ofX
1 is strictly larger than the entropy ofX
2, then there exists a finitary homomorphism ϕ:X
1→X
2 such that the code length is anL
p
random variable for allp<4/3. In particular, the expected length of the code ϕ is finite.
Research supported by KBN grant 2 P03A 039 15 1998–2001. 相似文献
18.
B. Wilkens 《Israel Journal of Mathematics》2009,172(1):357-369
Let P be a finite p-group, p a prime. We prove that there is a finite p-group Q ≥ P such that every normal subgroup of Q is characteristic in Q. 相似文献
19.
Eric S. Brussel 《Israel Journal of Mathematics》1996,96(1):141-183
LetF be a discretely Henselian field of rank one, with residue fieldk a number field, and letD/F be anF-division algebra. We conduct an exhaustive study of the decomposability of an arbitraryD. Specifically, we prove the following:D has a semiramified (SR)F-division subalgebra if and only ifD has a totally ramified (TR) subfield. However, there may be TR subfields not contained in any SR subalgebra. IfD has prime-power index, thenD is decomposable if and only ifD properly contains a SR division subalgebra. Equivalently,D has a decomposable Sylow factor if and only if ii(D
⊗n
)≠1/n
i(D) for somen dividing the period ofD, that is, if and only if the index fails to mimic the behavior of the period ofD. There exists indecomposableD with prime-power periodp
2 and indexp
3. Every proper division subalgebra ofD is indecomposable. Conversely, every indecomposableF-division algebra ofp-power index embeds properly in someD ofp-power index if and only ifk does not have a certain strengthened form of class field theory’s Special Case. Semiramified division algebras and division
algebras of odd index always properly embed. Finally, these results apply to an extent overk(t), and we prove that there exist indecomposablek(t)-division algebras of periodp
2 and indexp
3, solving an open problem of Saltman.
Dedicated to the memory of Amitsur
Research supported in part by NSF Grant DMS-9100148. 相似文献
20.
Jin Ke HAI Yi Xin ZHU 《数学学报(英文版)》2006,22(6):1751-1756
Alperin and Broug have given the p-subpairs in a finite group, and proved that there is a Sylow theorem for p-subpairs. For a π-separable group with π-Hall subgroup nilpotent, we prove that there is a π-Sylow theorem for π-subpairs. Note that our π-subpairs are different from what Robinson and Staszewski gave. 相似文献