Abstract
ItH i is a finite non-abelianp-group with center of orderp, for 1≦j≦R, then the direct product of theH i does not occur as a normal subgroup contained in the Frattini subgroup of any finitep-group. If the Frattini subgroup Φ of a finitep-groupG is cyclic or elementary abelian of orderp 2, then the centralizer of Φ inG properly contains Φ. Non-embeddability properties of products of groups of order 16 are established.
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