共查询到20条相似文献,搜索用时 234 毫秒
1.
Li Fang WANG Yan Ming WANG 《数学学报(英文版)》2007,23(11):1985-1990
Let З be a complete set of Sylow subgroups of a finite group G, that is, З contains exactly one and only one Sylow p-subgroup of G for each prime p. A subgroup of a finite group G is said to be З-permutable if it permutes with every member of З. Recently, using the Classification of Finite Simple Groups, Heliel, Li and Li proved tile following result:
If the cyclic subgroups of prime order or order 4 iif p = 2) of every member of З are З-permutable subgroups in G, then G is supersolvable.
In this paper, we give an elementary proof of this theorem and generalize it in terms of formation. 相似文献
2.
Shi Rong LI 《数学学报(英文版)》2005,21(4):797-802
For a finite group G, let T(G) denote a set of primes such that a prime p belongs to T(G) if and only if p is a divisor of the index of some maximal subgroup of G. It is proved that if G satisfies any one of the following conditions: (1) G has a p-complement for each p∈T(G); (2)│T(G)│= 2: (3) the normalizer of a Sylow p-subgroup of G has prime power index for each odd prime p∈T(G); then G either is solvable or G/Sol(G)≌PSL(2, 7) where Sol(G) is the largest solvable normal subgroup of G. 相似文献
3.
Zvonimir Janko 《Mathematische Zeitschrift》2006,254(1):29-31
In this note we consider finite noncyclic p-groups G all of whose maximal cyclic subgroups X satisfy one of the following two properties.
(a) If each subgroup H of G containing X properly is nonabelian, then p = 2 and G is generalized quaternion.
(b) If X is contained in exactly one maximal subgroup of G, then G is metacyclic.
This solves the problems Nr.1541 and Nr. 1594 from [1]. 相似文献
4.
We call a subgroup H of a finite group G c-supplemented in G if there exists a subgroup K of G such that G = HK and H ∩ K ⩽ core(H). In this paper it is proved that a finite group G is p-nilpotent if G is S
4-free and every minimal subgroup of P ∩ G
N
is c-supplemented in N
G
(P), and when p = 2 P is quaternion-free, where p is the smallest prime number dividing the order of G, P a Sylow p-subgroup of G. As some applications of this result, some known results are generalized. 相似文献
5.
Enrico Jabara 《Czechoslovak Mathematical Journal》2005,55(4):993-996
In this note we study finite p-groups G = AB admitting a factorization by an Abelian subgroup A and a subgroup B. As a consequence of our results we prove that if B contains an Abelian subgroup of index p
n−1 then G has derived length at most 2n. 相似文献
6.
We prove that a 2-group has exactly five rational irreducible characters if and only if it is dihedral, semidihedral or generalized quaternion. For an arbitrary prime p, we say that an irreducible character χ of a p-group G is “almost rational” if ℚ(χ) is contained in the cyclotomic field ℚ p , and we write ar(G) to denote the number of almost-rational irreducible characters of G. For noncyclic p-groups, the two smallest possible values for ar(G) are p 2 and p 2 + p − 1, and we study p-groups G for which ar(G) is one of these two numbers. If ar(G) = p 2 + p − 1, we say that G is “exceptional”. We show that for exceptional groups, |G: G′| = p 2, and so the assertion about 2-groups with which we began follows from this. We show also that for each prime p, there are exceptional p-groups of arbitrarily large order, and for p ≥ 5, there is a pro-p-group with the property that all of its finite homomorphic images of order at least p 3 are exceptional. 相似文献
7.
On permutable subgroups of finite groups 总被引:6,自引:0,他引:6
Let
\frak Z \frak Z be a complete set of Sylow subgroups of a finite group G, that is, for each prime p dividing the order of G,
\frak Z \frak Z contains exactly one and only one Sylow p-subgroup of G. A subgroup H of a finite group G is said to be
\frak Z \frak Z -permutable if H permutes with every member of
\frak Z \frak Z . The purpose here is to study the influence of
\frak Z \frak Z -permutability of some subgroups on the structure of finite groups. Some recent results are generalized. 相似文献
8.
Let ℱ be a class of groups and let G be a finite group. We call a set Σ of subgroups of G a covering subgroup system of G for ℱ (or directly an ℱ-covering subgroup system of G) if G ∈ ℱ whenever every subgroup in Σ is in ℱ. We give some covering subgroup systems for the class of all p-nilpotent groups. 相似文献
9.
A subgroup H of a finite group
G is called c-normal in
G if there exists a normal subgroup
N of G such that
G = HN and $H \cap N \leq H_{G} = {\rm core}_{G}(H)$. In this paper, we investigate the class of groups
of which every maximal subgroup of its Sylow
p-subgroup is c-normal and the
class of groups of which some minimal subgroups of its Sylow
p-subgroup is c-normal for some prime number
p. Some interesting results are obtained and
consequently, many known results related to
p-nilpotent groups and
p-supersolvable groups are generalized. 相似文献
10.
Martin Hertweck 《代数通讯》2013,41(9):3224-3229
It is shown that in the units of augmentation one of an integral group ring ? G of a finite group G, a noncyclic subgroup of order p 2, for some odd prime p, exists only if such a subgroup exists in G. The corresponding statement for p = 2 holds by the Brauer–Suzuki theorem, as recently observed by Kimmerle. 相似文献
11.
Zhangjia Han 《Proceedings Mathematical Sciences》2010,120(2):141-148
A subgroup H of a group is said to be s-semipermutable in G if it is permutable with every Sylow p-subgroup of G with (p, |H|) = 1. Using the concept of s-semipermutable subgroups, some new characterizations of p-nilpotent groups are obtained and several results are generalized. 相似文献
12.
We determine the maximal number of conjugacy classes of maximal elementary abelian subgroups of rank 2 in a finite p-group G, for an odd prime p. Namely, it is p if G has rank at least 3 and it is p+1 if G has rank 2. More precisely, if G has rank 2, there are exactly 1,2,p+1, or possibly 3 classes for some 3-groups of maximal nilpotency class. 相似文献
13.
In this paper it is proved that ifp is a prime dividing the order of a groupG with (|G|,p − 1) = 1 andP a Sylowp-subgroup ofG, thenG isp-nilpotent if every subgroup ofP ∩G
N
of orderp is permutable inN
G
(P) and whenp = 2 either every cyclic subgroup ofP ∩G
N
of order 4 is permutable inN
G
(P) orP is quaternion-free. Some applications of this result are given.
The research of the first author is supported by a grant of Shanxi University and a research grant of Shanxi Province, PR
China.
The research of the second author is partially supported by a UGC(HK) grant #2160126 (1999/2000). 相似文献
14.
A subgroup H of a finite group G is said to be c*-supplemented in G if there exists a subgroup K such that G = HK and H ⋂ K is permutable in G. It is proved that a finite group G that is S
4-free is p-nilpotent if N
G
(P) is p-nilpotent and, for all x ∈ G\N
G
(P), every minimal subgroup of
is c*-supplemented in P and (if p = 2) one of the following conditions is satisfied: (a) every cyclic subgroup of
of order 4 is c*-supplemented in P, (b)
, (c) P is quaternion-free, where P a Sylow p-subgroup of G and
is the p-nilpotent residual of G. This extends and improves some known results.
Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 8, pp. 1011–1019, August, 2007. 相似文献
15.
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
16.
Let A be a subgroup of a group G and X be a nonempty subset of G. A is said to be X-semipermutable in G if A has a supplement T in G such that A is X-permutable with every subgroup of T. In this paper, we investigate further the influence of X-semipermutability of some subgroups on the structure of finite groups. Some new criteria for a group G to be supersoluble or p-nilpotent are obtained.
This work was supported by National Natural Science Foundation of China (Grant Nos. 10771172, 10771180) 相似文献
17.
Yun Fan 《Mathematische Zeitschrift》2003,243(2):355-389
In a G-algebra A of a p-group G over a perfect ground field there is a commutative separable semisimple G-subalgebra such that any traces on relative projectivity in A can be controlled in the subalgebra; and in a residually central sense, the maximal such subalgebras form exactly one -conjugacy class. Applying to modules, the induced module of an indecomposable module of a subnormal subgroup of p- primary index is characterized.
Received: 13 April 2002 / Published online: 2 December 2002 相似文献
18.
Changwen Li 《印度理论与应用数学杂志》2011,42(5):291-306
A subgroup of H of a group G is called ss-quasinormally embedded in G if there exists a subgroup T of G such that G = HT and H ∩ T is squasinormally embedded in G. In this paper, we shall obtain some characterizations about p-nilpotency of G by assuming that some subgroups of prime power order of G are ss-quasinormally embedded in G. 相似文献
19.
Hongfei Pan 《代数通讯》2017,45(12):5374-5379
Let G be a finite group and n be a positive integer. An n-minimal subgroup H of G is called to be exactly n-minimal if no proper subgroup of H is n-minimal. In this paper, we study the solvability of G under the assumption that all exactly n-minimal subgroups of G are S-permutable. 相似文献
20.
Takashi Okuyama 《代数通讯》2013,41(1):121-139
We determine the structure of a p-pure[pure] hull of a p-purifiable [purifiable] subgroup of an arbitrary abelian group. Moreover, we prove that a subgroup A of an abelian group G is purifiable in G if and only if A is p-purifiable in G for every prime p. Using these results, we characterize the groups G for which all subgroups are purifiable in G. Furthermore, we establish several properties of purifiable subgroups. 相似文献