In this work, we derive closed-form expression for the Gallager’s random coding error exponent for a MIMO multiple-scattering channel. The number of scattering stages is arbitrary but finite, white noise is present at the destination.

This paper deals with the number of subgroups of a given exponent in a finite abelian group. Explicit formulas are obtained in the case of rank two and rank three abelian groups. An asymptotic formula is also presented.

We study the commuting graph on elements of odd prime order in finite simple groups. The results are used in a forthcoming paper describing the structure of Bruck loops and Bol loops of exponent 2.

We study the finite-size effects in some scaling systems, and show that the finite number of agents N leads to a cut-off in the upper value of the Pareto law for the relative individual wealth. The exponent α of the Pareto law obtained in stochastic multiplicative market models is crucially affected by the fact that N is always finite in real systems. We show that any finite value of N leads to...

Let p be a prime. A group is called p-closed if it has a normal Sylow p-subgroup and it is called p-exponent closed if the elements of order dividing p form a subgroup. A group is minimal non-p-closed if it is not p-closed but its proper subgroups and homomorphic images are. Similarly, a group is called minimal non-p-exponent closed if it is not p-exponent closed but all its proper subgroups an...

Abstract We improve the exponent in finite field sum-product problem from $11/9$ to $5/4$, improving results of Rudnev et al. [16]. That is, we show that if $A\subset \mathbb {F}_p$ has cardinality $|A|\ll p^{1/2}$, then $ \max \{|A\pm A|,|AA|\} \gtrsim |A|^\frac 54 and A|,|A/A|\}\gtrsim $.