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31.
Let G be a non-abelian group and Z(G) be the center of G. The non-commuting graph Γ G associated to G is the graph whose vertex set is G?Z(G) and two distinct elements x, y are adjacent if and only if xy ≠ yx. We prove that if G and H are non-abelian nilpotent groups with irregular isomorphic non-commuting graphs, then |G| = |H|. 相似文献
32.
Ahmed Hegazi 《代数通讯》2013,41(12):5237-5256
The paper is devoted to the study of annihilator extensions of Jordan algebras and suggests new approach to classify nilpotent Jordan algebras, which is analogous to the Skjelbred–Sund method for classifying nilpotent Lie algebras [2, 4, 15]. Subsequently, we have classified nilpotent Jordan algebras of dimension up to four. 相似文献
33.
We define nilpotent and strongly nilpotent elements of a module M and show that the set 𝒩 s (M) of all strongly nilpotent elements of M over a commutative unital ring R coincides with the classical prime radical β cl (M) the intersection of all classical prime submodules of M. 相似文献
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Maria V. Milentyeva 《代数通讯》2013,41(4):1141-1154
We obtain the functions that bound the dimensions of finite dimensional nilpotent associative or Lie algebras of class 2 over an algebraically closed field in terms of the dimensions of their commutative subalgebras. As a result, we also compute a similar function for complex nilpotent Lie groups of class 2. 相似文献
37.
K. R. McLean 《代数通讯》2013,41(12):4427-4439
A group G is (l,m,n)-generated if it is a quotient group of the triangle group T(l,m,n) = (x,y,z|x l= y m= z n= xyz= 1). In [8] the problem is posed to find all possible (l,m,n)-generations for the non-abelian finite simple groups. In this paper we partially answer this question for the Janko group J 3. We find all (2, 3, t)-generations as well as (2, 2,2,p)-generations, p a prime, for J 3 相似文献
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Binyong Hsie 《代数通讯》2013,41(10):3743-3750
In this article, the author gives two methods to construct complete Lie algebras. Both methods show that the derivation algebras of some Lie algebras are complete. 相似文献
40.
It is proved that if a (?/p ?)-graded Lie algebra L, where p is a prime, has exactly d nontrivial grading components and dim L 0 = m, then L has a nilpotent ideal of d-bounded nilpotency class and of finite (m,d)-bounded codimension. As a consequence, Jacobson's theorem on constant-free nilpotent Lie algebras of derivations is generalized to the almost constant-free case. Another application is for Lie algebras with almost fixed-point-free automorphisms. 相似文献