A problem of Gratzer and Wehrung on groups

Research Report MRR98-011

A problem of Grätzer and Wehrung on groups

L. G. Kovács, B. H. Neumann and M. F. Newman

Abstract: Given a group G, is there a group $\ol G$ which contains G as a proper subgroup and is such that every nontrivial normal subgroup N of G can be uniquely represented in the form $\ol{N}\cap G$ with $\ol{N}$ a normal subgroup of $\ol G$ ? The answer is negative for elementary abelian G of prime-square order, but is positive for all G if one allows two such representations when N=1.

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