Speaker:翟文广（中国矿业大学（北京）） Venue: B1044 Time: 2017年10月12日 10:30-11:30 Title:On the average number of subgroups of $Z_m times Z_n$ Abstract:Let $Z_m$ be the additive group of residue classes modulo $m.$ For any positive integers $m$ and $n$, let $s(m,n)$   and $c(m,n)$ denote the number of subgroups and the number of   cyclic subgroups of the group $Z_mtimes Z_n$, respectively. We shall study the asymptotic behavior of the sums   $sum_{m,nleq x}s(m,n)$ and $sum_{m,nle x}c(m,n)$.