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991.
In this article, we show that a group is abelian if and only if every two elements of the same order commute. 相似文献
992.
Sunsook Noh 《代数通讯》2013,41(2):613-624
Let υ be a prime divisor of a 2-dimensional regular local ring (R m) with algebraically closed residue field k. Zariski showed that a prime divisor υ of R is uniquely associated to a simple m-primary integrally closed ideal I of R, there exist finitely many simple υ-ideals including I, and all the other υ-ideals can be uniquely factored into products of simple υ-ideals. It is known that such an m-primary ideal I of R can be minimally generated by o(I) + 1 elements.Given a simple integrally closed ideal I of order one with arbitrary rank and its associated prime divisor υ, we find minimal generating sets of all the simple υ-ideals and describe factorizations of all the composite υ-ideals in terms of power products of simple υideals as explicitly as possible. 相似文献
993.
994.
Over a commutative ring R with identity, free modules M with 2 distinguished submodules are studied. The category Rep2R of such objects M have the obvious morphisms between them, which are homomorphisms between .R-modules preserving the distinguished submodules. The endo-morphisms for each M constitute a subalgebra EndRM of the algebra EndRM and the readability of λ-generated R-algebras A as EndRM is considered for cardinals λ. Despite the fact that 4 is the minimal number of distinguished submodules for realizing any algebra over a field il, we are able to prove a similar result in Rep2R for many rings R including R = Z and algebras which are cotorsion-free. Several examples illustrate the boarder line of our main result. The main theorem is applied for constructing Butler groups in [11] 相似文献
995.
Annette Pilkington 《代数通讯》2013,41(9):3183-3202
This article investigates several convex closure operators on a finite root system. It is shown that a natural closure operator on the positive root system of a finite Weyl group satisfies the anti-exchange condition for all root systems except type F 4. 相似文献
996.
J. Cimprič 《代数通讯》2013,41(1):103-119
A subgroup H is called Q-supplemented in a finite group G, if there exists a subgroup K of G such that G = HK and H ∩ K is contained in H QG , where H QG is the maximal quasinormal subgroup of G contained in H. In this article, we investigate the influence of Q-supplementation of some primary subgroups in finite groups. Some recent results are generalized. 相似文献
997.
Motiejus Valiunas 《代数通讯》2013,41(12):5101-5120
998.
Victor Guba 《代数通讯》2013,41(5):1988-1997
Let G be a group generated by a finite set A. An element g ∈ G is a strict dead end of depth k (with respect to A) if |g|>|ga 1|>|ga 1 a 2|>···>|ga 1 a 2… a k | for any a 1, a 2,…, a k ∈ A ±1 such that the word a 1 a 2… a k is freely irreducible. (Here |g| is the distance from g to the identity in the Cayley graph of G.) We show that in finitely generated free soluble groups of degree d ≥ 2 there exist strict dead elements of depth k = k(d), which grows exponentially with respect to d. 相似文献
999.
AbstractIn this note we prove that the Eaton-Moretó conjecture holds for all blocks of finite general linear and unitary groups for all primes. Also, we show that no block of a finite quasi-simple group of classical Lie type provides a minimal counterexample to the conjecture, and so for ? > 5 no ?-block of any quasi-simple group can be a minimal counterexample. 相似文献
1000.
Peter Davidson 《代数通讯》2013,41(4):1448-1459
Pride groups are defined by means of finite (simplicial) graphs, and examples include Artin groups, Coxeter groups, and generalized tetrahedron groups. Under suitable conditions, we calculate an upper bound of the first order Dehn function for a finitely presented Pride group. We thus obtain sufficient conditions for when finitely presented Pride groups have solvable word problems. As a corollary to our main result, we show that the first order Dehn function of a generalized tetrahedron group, containing finite generalized triangle groups, is at most cubic. 相似文献