If is a perfect group, then the group center of the quotient group , where is the group center of , is the trivial group.
Grün's Lemma
See also
Perfect GroupThis entry contributed by Margherita Barile
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References
Rose, J. S. A Course in Group Theory. New York: Dover, p. 61, 1994.Referenced on Wolfram|Alpha
Grün's LemmaCite this as:
Barile, Margherita. "Grün's Lemma." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/GruensLemma.html