Stewart Stonehewer, Giovanni Zacher
June 15, 2009
Given a group G and subgroups X ⩾ Y , with Y of finite index in X , then in general it is not possible to determine the index | X : Y | simply from the lattice of subgroups of G . For example, this is the case when G has prime order. The purpose of this work is twofold. First we show that in any group, if the indices | X : Y | are determined for all cyclic subgroups X , then they are determined for all subgroups X . Second we show that if G is a group with an ascending normal series with factors locally finite or abelian, and if the Hirsch length of G is at least 3, then all indices | X : Y | are determined.