On finite groups with disconnected prime graph

All finite simple nonabelian groups that have the same prime graph as a Frobenius group or a 2-Frobenius group are found.     

Circular autowaves in human atria and initial conditions for their emergence

Systems of nonlinear parabolic partial differential equations were used for a computational study of circular self-oscillatory processes in the active medium of the atria. The FitzHugh-Nagumo nonlinear differential equation was used in this work. The following excitation pathways of circular reentry waves were considered: 1. Excitation combined with unilateral blockade of excitation; 2. The effect of a part of a simple autowave; 3. Excitation in the tail part of the autowave; and 4. Emergence of a temporarily refractory site in the fixed part of a channel. The pathways of circular autowave excitation listed above provide a comprehensive representation of the currently characterized excitation pathways for this type of wave. The results of computational experiments that illustrate the excitation pathways of circular reentry waves are reported in this work.     

Groups with given properties of finite subgroups

Suppose that in every finite even order subgroup F of a periodic group G, the equality [u, x]² = 1 holds for any involution u of F and for an arbitrary element x of F. Then the subgroup I generated by all involutions in G is locally finite and is a 2-group. In addition, the normal closure of every subgroup of order 2 in G is commutative.