Parameterizing solutions to any Galois embedding problem over<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:mi mathvariant="double-struck">Z</mml:mi><mml:mo stretchy="false">/</mml:mo><mml:msup><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msup><mml:mi mathvariant="double-struck">Z</mml:mi></mml:math>with elementary p -abelian kernel