Rational and nilpotent implies 2-group: Difference between revisions
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* [[Rational and abelian implies elementary abelian 2-group]] | * [[Rational and abelian implies elementary abelian 2-group]] | ||
==Facts used== | |||
# [[uses::Ambivalent and nilpotent implies 2-group]] | |||
# [[uses::Rational implies ambivalent]] | |||
==Proof== | |||
The proof follows directly from Facts (1) and (2). | |||
Latest revision as of 02:14, 13 January 2013
Statement
Suppose is a group that is both a Rational group (?) and a Nilpotent group (?). Then, must be a 2-group, i.e., it is a group in which every element has finite order and the order is a power of 2.
Related facts
Facts used
Proof
The proof follows directly from Facts (1) and (2).