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A note on a class of factorized p -groups

Enrico Jabara (2005)

Czechoslovak Mathematical Journal

In this note we study finite p -groups G = A B admitting a factorization by an Abelian subgroup A and a subgroup B . As a consequence of our results we prove that if B contains an Abelian subgroup of index p n - 1 then G has derived length at most 2 n .

A note on a theorem of Megibben

Peter Vassilev Danchev, Patrick Keef (2008)

Archivum Mathematicum

We prove that pure subgroups of thick Abelian p -groups which are modulo countable are again thick. This generalizes a result due to Megibben (Michigan Math. J. 1966). Some related results are also established.

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