Endomorphisms of free metabelian Lie algebras which preserve orbits.

Chirkov, I.V.; Shevelin, M.A.

Displaying similar documents to “Endomorphisms of free metabelian Lie algebras which preserve orbits.”

On tame automorphisms of some metabelian groups.

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A nilpotent ideal in the Lie rings with automorphism of prime order.

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On universal theories of metabelian groups and the Shmel'kin embedding.

Timoshenko, E.I. (2001)

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On solvability of Lie rings with an automorphism of finite order.

Khukhro, E.I. (2001)

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On generators of free color Lie superalgebras of rank two.

Aydın, Ela, Ekici, Naime (2002)

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Mild 2-relator pro- $p$ -groups.

Bush, Michael R., Gärtner, Jochen, Labute, John, Vogel, Denis (2011)

The New York Journal of Mathematics [electronic only]

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Modified proof of a local analogue of the Grothendieck conjecture

Victor Abrashkin (2010)

Journal de Théorie des Nombres de Bordeaux

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A local analogue of the Grothendieck Conjecture is an equivalence between the category of complete discrete valuation fields $K$ with finite residue fields of characteristic $p \neq 0$ and the category of absolute Galois groups of fields $K$ together with their ramification filtrations. The case of characteristic 0 fields $K$ was studied by Mochizuki several years ago. Then the author of this paper proved it by a different method in the case $p > 2$ (but with no restrictions on the characteristic of $K$ )....

Primes, permutations and primitive roots.

Lewittes, Joseph, Kolyvagin, Victor (2010)

The New York Journal of Mathematics [electronic only]

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Fibonacci numbers and Fermat's last theorem

Zhi-Wei Sun (1992)

Acta Arithmetica

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Let Fₙ be the Fibonacci sequence defined by F₀=0, F₁=1, $F_{n + 1} = F ₙ + F_{n - 1} (n \geq 1)$ . It is well known that $F_{p - (5 / p)} \equiv 0 (m o d p)$ for any odd prime p, where (-) denotes the Legendre symbol. In 1960 D. D. Wall [13] asked whether $p ² | F_{p - (5 / p)}$ is always impossible; up to now this is still open. In this paper the sum $\sum_{k \equiv r (m o d 10)} (\binom{n}{k})$ is expressed in terms of Fibonacci numbers. As applications we obtain a new formula for the Fibonacci quotient $F_{p - (5 / p)} / p$ and a criterion for the relation $p | F_{(p - 1) / 4}$ (if p ≡ 1 (mod 4), where p ≠ 5 is an odd prime. We also prove that the affirmative...

On metabelian groups with derived quotient an elementary Abelian 2-group of rank 3.

Bludov, V.V., Dolbak, L.V. (2007)

Sibirskie Ehlektronnye Matematicheskie Izvestiya [electronic only]

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On integers not of the form n - φ (n)

J. Browkin, A. Schinzel (1995)

Colloquium Mathematicae

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W. Sierpiński asked in 1959 (see [4], pp. 200-201, cf. [2]) whether there exist infinitely many positive integers not of the form n - φ(n), where φ is the Euler function. We answer this question in the affirmative by proving Theorem. None of the numbers $2^{k} \cdot 509203$ (k = 1, 2,...) is of the form n - φ(n).