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Paper   IPM / M / 16585
School of Mathematics
  Title:   Minimal partition-free groups
  Author(s):  Zeinab Akhlaghi (Joint with A. Bahri and B. Khosravi)
  Status:   To Appear
  Journal: Ricerche mat.
  Supported by:  IPM
Let G be a finite group. A collection P = H1; ... ;Hr of subgroups of G, where r > 1, is said a non-trivial partition of G if every non-identity element of G belongs to one and only one Hi, for some 1 <=i<= r. We call a group G that does not admit any non-trivial partition a partition-free group. In this paper, we study a partition-free group G whose all proper non-cyclic subgroups admit non-trivial partitions.

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