arXiv subjects

Ron Brown

Publications and source records attributed to Ron Brown.

2 recordsLinked to original sources

arXiv2021

The natural density of some sets of square-free numbers

Let $P$ and $T$ be disjoint sets of prime numbers with $T$ finite. A simple formula is given for the natural density of the set of square-free numbers which are divisible by all of the primes in $T$ and by none of the primes in $P$. If $P$ is the set of primes congruent to $r$ modulo $m$ (where $m$ and $r$ are relatively prime numbers), then this natural density is shown to be $0$.

math.NT↗

arXiv2021

Many Frobenius complements have even order

The theory of Frobenius groups with Frobenius complements of even order largely reduces to tractable algebraic number theory. If we consider only Frobenius complements with an upper bound $s$ on the number of distinct primes dividing the order of their commutator subgroups, then the proportion of these with odd order is less than $1/2^{s}$. A positive lower bound is also given.

math.GR↗