Characterization of simple symplectic groups of degree 4 over locally finite fields of characteristic 2 in the class of periodic groups

Suppose that each finite subgroup of even order of a periodic group containing an element of order 2 lies in a subgroup isomorphic to a simple symplectic group of degree 4 over some finite field of characteristic 2. We prove that in that case the group is isomorphic to a simple symplectic group S ₄(Q) over some locally finite field Q of characteristic 2.     

Heavy ion linear accelerator with high-frequency quadrupole focusing

Based on results of works on the NICA/MPD (Joint Institute for Nuclear Research, Dubna) project, the possibility of designing a heavy ion linear accelerator with high-frequency quadrupole focusing both in the input part and in the main part of the accelerator is shown. Parameters of the linear ¹⁹⁷Au³¹⁺ ion accelerator are presented. Special attention is paid to technical questions of calculating, designing, manufacturing, and tuning the accelerator.     

On stationary classes of three-value logic functions

This work is devoted to the properties of transformations of the vector of values of three-value logic functions to the vector of coefficients of their polynomials. A similar transformation of Boolean functions is used in cryptology, and its properties have been thoroughly studied. Stationary classes of three-value logic functions are introduced, and their hierarchy and the exact number of functions in them are obtained.     

On 2-groups with finite subgroups of rank 2

A classification is achieved of the 2-groups all of whose finite subgroups are generated by two elements.     

Minimal permutation representations of finite simple classical groups. Special linear,symplectic, and unitary groups

This work was supported by the Russian Foundation for Fundamental Research, grant 93-011-1501.     

Minimal permutation representations of finite simple orthogonal groups

In the paper, nontrivial permutation representations of minimal degree are studied for finite simple orthogonal groups. For them, we find degrees, ranks, subdegrees, point stabilizers and their pairwise intersections.Translated fromAlgebra i Logika, Vol. 33, No. 6, pp. 603–627, November–December, 1994.     

A question of L. A. Shemetkov

Translated fromAlgebra i Logika, Vol. 31, No. 6, pp. 624–636, November–December, 1992.     

Recognition of finite groups by a set of orders of their elements

For G a finite group, ω(G) denotes the set of orders of elements in G. If ω is a subset of the set of natural numbers, h(ω) stands for the number of nonisomorphic groups G such that ω(G)=ω. We say that G is recognizable (by ω(G)) if h(ω(G))=1. G is almost recognizable (resp., nonrecognizable) if h(ω(G)) is finite (resp., infinite). It is shown that almost simple groups PGL_n(q) are nonrecognizable for infinitely many pairs (n, q). It is also proved that a simple group S₄(7) is recognizable, whereas A₁₀, U₃(5), U₃(7), U₄(2), and U₅(2) are not. From this, the following theorem is derived. Let G be a finite simple group such that every prime divisor of its order is at most 11. Then one of the following holds: (i) G is isomorphic to A₅, A₇, A₈, A₉, A₁₁, A₁₂, L₂(q), q=7, 8, 11, 49, L₃(4), S₄(7), U₄(3), U₆(2), M₁₁, M₁₂, M₂₂, HS, or M^cL, and G is recognizable by the set ω(G); (ii) G is isomorphic to A₆, A₁₀, U₃(3), U₄(2), U₅(2), U₃(5), or J₂, and G is nonrecognizable; (iii) G is isomorphic to S₆(2) or O ₈ ⁺ (2), and h(ω(G))=2. Supported by RFFR grant No. 96-01-01893. Translated fromAlgebra i Logika, Vol. 37, No. 6, pp. 651–666, November–December, 1998.