Nilpotent Numbers
نویسندگان
چکیده
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منابع مشابه
Orders for Which There Exist Exactly Two Groups
Introduction. A long-standing problem in group theory is to determine the number of non-isomorphic groups of a given order. The inverse problem–determining the orders for which there are a given number of groups–has received considerably less attention. In this note, we will give a characterization of those positive integers n for which there exist exactly 2 distinct groups of order n (up to is...
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Introduction. One of the first things we learn in abstract algebra is the notion of a cyclic group. For every positive integer n, we have Zn, the group of integers modulo n. When n is prime, a simple application of Lagrange’s theorem yields that this is the only group of order n. We may ask ourselves: what other positive integers have this property? In this spirit we call a positive integer n a...
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We consider Mn(R), the ring of n by n matrices on the real numbers where n ≥ 2. We find all of the natural numbers that are the degree of nilpotency of some nilpotent derivations on Mn(R). Mathematics Subject Classification: 16S50, 13N15, 16N40
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We compute the numbers g(n, 2, 2) of nilpotent groups of order n, of class at most 2 generated by at most 2 generators, by giving an explicit formula for the Dirichlet generating function P
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This is an expository article on the singularities of nilpotent orbit closures in simple Lie algebras over the complex numbers. It is slanted towards aspects that are relevant for representation theory, including Ma ei's theorem relating Slodowy slices to Nakajima quiver varieties in type A. There is one new observation: the results of Juteau and Mautner, combined with Ma ei's theorem, give a g...
متن کاملThe Asymptotic Density of Finite-order Elements in Virtually Nilpotent Groups
Let Γ be a finitely generated group with a given word metric. The asymptotic density of elements in Γ that have a particular property P is the limit, as r → ∞, of the proportion of elements in the ball of radius r which have the property P . We obtain a formula to compute the asymptotic density of finite-order elements in any virtually nilpotent group. Further, we show that the spectrum of numb...
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ورودعنوان ژورنال:
- The American Mathematical Monthly
دوره 107 شماره
صفحات -
تاریخ انتشار 2000