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Change definition of IsPGroup to *not* require finiteness #1545

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May 15, 2018
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Change definition of IsPGroup to *not* require finiteness #1545

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13 changes: 10 additions & 3 deletions lib/grp.gd
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Expand Up @@ -415,11 +415,18 @@ DeclareOperation( "KnowsHowToDecompose", [ IsGroup, IsList ] );
##
## <Description>
## <Index Key="p-group"><M>p</M>-group</Index>
## A <E><M>p</M>-group</E> is a finite group whose order
## (see&nbsp;<Ref Func="Size"/>) is of the form <M>p^n</M> for a prime
## integer <M>p</M> and a nonnegative integer <M>n</M>.
## A <E><M>p</M>-group</E> is a group in which the order
## (see&nbsp;<Ref Func="Order"/>) of every element is of the form <M>p^n</M>
## for a prime integer <M>p</M> and a nonnegative integer <M>n</M>.
## <Ref Prop="IsPGroup"/> returns <K>true</K> if <A>G</A> is a
## <M>p</M>-group, and <K>false</K> otherwise.
## <P/>
## Finite <M>p</M>-groups are precisely those groups whose order
## (see&nbsp;<Ref Func="Size"/>) is a prime power, and are always
## nilpotent.
## <P/>
## Note that <M>p</M>-groups can also be infinite, and in that case,
## need not be nilpotent.
## </Description>
## </ManSection>
## <#/GAPDoc>
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