共查询到20条相似文献,搜索用时 31 毫秒
1.
For a finite p-group G and a positive integer k let I
k
(G) denote the intersection of all subgroups of G of order p
k
. This paper classifies the finite p-groups G with Ik(G) @ Cpk-1{{I}_k(G)\cong C_{p^{k-1}}} for primes p > 2. We also show that for any k, α ≥ 0 with 2(α + 1) ≤ k ≤ n−α the groups G of order p
n
with Ik(G) @ Cpk-a{{I}_k(G)\cong C_{p^{k-\alpha}}} are exactly the groups of exponent p
n-α
. 相似文献
2.
Primož Moravec 《Israel Journal of Mathematics》2009,174(1):19-28
We prove that the nonabelian tensor square of a powerful p-group is again a powerful p-group. Furthermore, If G is powerful, then the exponent of G ⊕ G divides the exponent of G. New bounds for the exponent, rank, and order of various homological functors of a given finite p-group are obtained. In particular, we improve the bound for the order of the Schur multiplier of a given finite p-group obtained by Lubotzky and Mann. 相似文献
3.
Yakov Berkovich 《Israel Journal of Mathematics》2013,194(2):831-869
We study the subgroup structure of some two-generator p-groups and apply the obtained results to metacyclic p-groups. For metacyclic p-groups G, p > 2, we do the following: (a) compute the number of nonabelian subgroups with given derived subgroup, show that (ii) minimal nonabelian subgroups have equal order, (c) maximal abelian subgroups have equal order, (d) every maximal abelian subgroup is contained in a minimal nonabelian subgroup and all maximal subgroups of any minimal nonabelian subgroup are maximal abelian in G. We prove the same results for metacyclic 2-groups (e) with abelian subgroup of index p, (f) without epimorphic image ? D8. The metacyclic p-groups containing (g) a minimal nonabelian subgroup of order p 4, (h) a maximal abelian subgroup of order p 3 are classified. We also classify the metacyclic p-groups, p > 2, all of whose minimal nonabelian subgroups have equal exponent. It appears that, with few exceptions, a metacyclic p-group has a chief series all of whose members are characteristic. 相似文献
4.
Let G be a finite group of order n, for some n\geqq 1 n\geqq 1 , and p be an odd prime number. In [5] Verardi has constructed a special p-group PG P_G of exponent p such that |PG|=p3n |P_G|=p^{3n} . In this paper, we calculate the order of Aut(PG) (P_G) and prove that Aut(PG) (P_G) is the semidirect product of two subgroups. 相似文献
5.
In §2, we prove that if a 2-group G and all its nonabelian maximal sub-groups are two-generator, then G is either metacyclic or minimal non-abelian. In §3, we consider a similar question for p > 2. In §4 the 2-groups all of whose minimal nonabelian subgroups have order 16 and a cyclic subgroup of index 2, are classified.
It is proved, in §5, that if G is a nonmetacyclic two-generator 2-group and A, B, C are all its maximal subgroups with d(A) ≤ d(B) ≤ d(C), then d(C) = 3 and either d(A) = d(B) = 3 (this occurs if and only if G/G′ has no cyclic subgroup of index 2) or else d(A) = d(B) = 2. Some information on the last case is obtained in Theorem 5.3. 相似文献
6.
LetR
n be n-dimensional Euclidean space with n>-3. Demote by Ω
n
the unit sphere inR
n. ForfɛL(Ω
n
) we denote by σ
N
δ
its Cesàro means of order σ for spherical harmonic expansions. The special value
l = \tfracn - 22\lambda = \tfrac{{n - 2}}{2}
of σ is known as the critical one. For 0<σ≤λ, we set
p0 = \tfrac2ld+ lp_0 = \tfrac{{2\lambda }}{{\delta + \lambda }}
.
This paper proves that
limN ? ¥ || sNd (f) - f ||p0 = 0\mathop {\lim }\limits_{N \to \infty } \left\| {\sigma _N^\delta (f) - f} \right\|p_0 = 0 相似文献
7.
Primo? Moravec 《Israel Journal of Mathematics》2011,185(1):189-205
In this paper we obtain bounds for the order and exponent of the Schur multiplier of a p-group of given coclass. These are further improved for p-groups of maximal class. In particular, we prove that if G is p-group of maximal class, then |H
2(G, ℤ)| < |G| and expH
2(G, ℤ) ≤ expG. The bound for the order can be improved asymptotically. 相似文献
8.
Gail L. Lange 《Israel Journal of Mathematics》1978,29(4):357-360
This paper deals with nonabelianp-groupsT (p a prime andp>2) which are either metacyclic or Redei. These groups are classified into those which are Frattini subgroups of a finitep-groupG and those which are not. Finally, it is shown that a nonabelian two-generator group of orderp
n
(n>4) which is the Frattini subgroup of ap-group must be metacyclic.
This work is contained in the author’s dissertation. 相似文献
9.
Zdravka Božikov 《Archiv der Mathematik》2006,86(1):11-15
According to a classical result of Burnside, if G is a finite 2-group, then the Frattini subgroup Φ(G) of G cannot be a nonabelian group of order 8. Here we study the next possible case, where G is a finite 2-group and Φ(G) is nonabelian of order 16. We show that in that case Φ(G) ≅ M × C2, where M ≅ D8 or M ≅ Q8 and we shall classify all such groups G (Theorem A).
Received: 16 February 2005; revised: 7 March 2005 相似文献
10.
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
11.
We show that if λ
1,λ
2,λ
3,λ
4 are nonzero real numbers, not all of the same sign, η is real, and at least one of the ratios λ
1/λ
j
(j=2,3,4) is irrational, then given any real number ω>0, there are infinitely many ordered quadruples of primes (p
1,p
2,p
3,p
4) for which
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