Blowdown Maps between Subgroup Posets

Abstract

To investigate the interrelationship between the subgroup posets of groups, we introduce poset-blowdowns between subgroup posets, motivated by blowdowns in algebraic geometry. Poset-blowdowns are divided into three types (tame, wild, hybrid) depending on their combinatorial properties. We provide various criteria for determining types. Moreover we completely classify tame types for finite groups: they are associated with either generalized quaternion groups or cyclic groups of prime power orders.