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81.
82.
A subgroup A of a finite group G is called a TI-subgroup if either A ∩ A x = 1 or A ∩ A x = A holds for all x ∈ G. In this paper, finite group all of whose meta-cyclic subgroups are TI-subgroups are classified completely. In particular, such groups are solvable. 相似文献
83.
《代数通讯》2013,41(2):789-798
We introduce the concept of decimal extension of the additive group of integers. We characterize these extensions as the linearly ordered abelian groups containing at least one Archimedean element. Finally, we study the additive group of rationals and its subgroups as particular cases of decimal extension. 相似文献
84.
Bangming Deng 《代数通讯》2013,41(10):3419-3434
Let G be a group and let N be a normal subgroup of G. We set cd(G|N) to be the degrees of the irreducible characters of G whose kernels do not contain N. We associate a graph with this set. The vertices of this graph are the primes dividing degrees in cd(G|N), and there is an edge between p and q if pq divides some degree in cd(G|N). In this paper, we study this graph when it is disconnected, and we study its diameter when it is connected. 相似文献
85.
《代数通讯》2013,41(9):3225-3238
ABSTRACT A cover for a group G is a collection of proper subgroups whose union is the whole group G. A cover is irredundant if no proper sub-collection is also a cover, and is called maximal if all its members are maximal subgroups. For an integer n > 2, a cover with n members is called an n-cover. Also, we denote σ (G) = n if G has an n-cover and does not have any m-cover for each integer m < n. In this article, we completely characterize groups with a maximal irredundant 6-cover with core-free intersection. As an application of this result, we characterize the groups G with σ (G) = 6. The intersection of an irredundant n-cover is known to have index bounded by a function of n, though in general the precise bound is not known. We also prove that the exact bound is 36 when n is 6. 相似文献
86.
Mong-Lung Lang 《代数通讯》2013,41(8):3691-3702
We determine the signatures of the congruence subgroups of the Hecke groups G 4 and G 6. 相似文献
87.
The sizes of Boolean combinations of subgroups G
i
of a finite abelian group depends only on the Boolean expression, the 0-1-sublattice generated by the G
i
, and the size of minimal subquotients from this sublattice. Moreover, they increase, monotonically, with those sizes. 相似文献
88.
N. S. Chernikov 《Mathematical Notes》2000,68(2):270-277
By analogy with π-minimal, π-layer minimal, primary minimal, and layer minimal conditions, similar maximal conditions are
introduced and studied.
Translated fromMatematicheskie Zametki, Vol. 68, No. 2, pp. 311–320, August, 2000. 相似文献
89.
Let G be a finite group, and let p1,…, pm be the distinct prime divisors of |G|. Given a sequence 𝒫 =P1,…, Pm, of Sylow pi-subgroups of G, and g ∈ G, denote by m𝒫(g) the number of factorizations g = g1…gm such that gi ∈ Pi. The properly normalized average of m𝒫 over all 𝒫 is a complex character over G whose kernel contains the solvable radical of G [7]. The present paper characterizes the solvable residual of G in terms of this character. 相似文献
90.
Andreas Weber 《Mathematical Physics, Analysis and Geometry》2009,12(1):75-95
We determine the L
p
spectrum of the Laplace-Beltrami operator on certain complete locally symmetric spaces M whose universal covering X is a symmetric space of non-compact type with rank one. More precisely, we show that the L
p
spectra of M and X coincide if the fundamental group of M is small and if the injectivity radius of M is bounded away from zero. In the L
2 case, the restriction on the injectivity radius is not needed.
相似文献