http://dspace.nbuv.gov.ua:80/handle/123456789/150358 2026-04-15T04:16:41Z http://dspace.nbuv.gov.ua:80/handle/123456789/154628 Frattini theory for N-Lie algebras Michael Peretzian Williams We develop a Frattini Theory for n-Lie algebras by extending theorems of Barnes' to the n-Lie algebra setting. Specifically, we show some sufficient conditions for the Frattini subalgebra to be an ideal and find an example where the Frattini subalgebra fails to be an ideal. 2009-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/154613 Commutative dimonoids Zhuchok, A.V. We present some congruence on the dimonoid with a commutative operation and use it to obtain a decomposition of a commutative dimonoid. 2009-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/154612 On some generalization of metahamiltonian groups Semko, N.N.; Yarovaya, O.A. Locally step groups at which all subgroups are or normal, or have Chernikov’s derived subgroup are studied. 2009-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/154610 On Galois groups of prime degree polynomials with complex roots Oz Ben-Shimol Let f be an irreducible polynomial of prime degree p≥5 over Q, with precisely k pairs of complex roots. Using a result of Jens Hochsmann (1999), show that if p≥4k+1 then Gal(f/Q) is isomorphic to Ap or Sp. This improves the algorithm for computing the Galois group of an irreducible polynomial of prime degree, introduced by A. Bialostocki and T. Shaska. If such a polynomial f is solvable by radicals then its Galois group is a Frobenius group of degree p. Conversely, any Frobenius group of degree p and of even order, can be realized as the Galois group of an irreducible polynomial of degree p over Q having complex roots. 2009-01-01T00:00:00Z