Abstract
LetK be a characteristic subgroup of ap-groupH such thatH induces onK a sufficiently large group of automorphisms. ThenH cannot be embedded as a normal subgroup contained in the Frattini subgroup in any finite group. The groupH may have a large center without any characteristic subgroup ofH properly contained in it. Examples are given for suchH withZ(H) elementary abelian of arbitrary dimension.
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Laue, R. On normalp-subgroups with large centers which cannot be contained in the Frattini subgroup. Israel J. Math. 29, 155–166 (1978). https://doi.org/10.1007/BF02762005
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DOI: https://doi.org/10.1007/BF02762005