Normal subgroup contained in the hypercenter satisfies the subgroup-to-quotient powering-invariance implication: Difference between revisions
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# [[uses::Powering-invariant and central implies quotient-powering-invariant]] | # [[uses::Powering-invariant and central implies quotient-powering-invariant]] | ||
# [[uses::Quotient-powering-invariance is quotient-transitive]] | # [[uses::Quotient-powering-invariance is quotient-transitive]] | ||
Revision as of 01:32, 13 February 2013
Statement
Suppose is a group and is a normal subgroup contained in the hypercenter of that is also a powering-invariant subgroup of . Then, is a quotient-powering-invariant subgroup of .
