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Yakov
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  • Member for 9 years
  • Last seen more than 8 years ago
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Normal abelian subgroups in p-groups
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Subgroups of the union of conjugates
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Which finite p-groups occur as commutators of finite p-groups?
If H is a two-generator p-group and $H\cong\Phi(G)$ for some p-group G, then H is metacyclic (known result).
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p-groups and 2-generated abelian images
Any extraspecial group of order $>p^3$ satisfies this condition.
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Center of finite metabelian p-groups
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A finite $p$-group with certain properties
In the first Geoff Robinson's example (there $A=\Phi(G)$), the class of B is p-1<p and so his group does not satisfy (c).
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