7.56 IsElementaryAbelian

IsElementaryAbelian( G )

IsElementaryAbelian returns true if the group G is an elementary abelian p-group for a prime p and false otherwise.

A p-group G is elementary abelian if and only if for every g, h in <G> the equations g* h = h* g and g^p = 1 hold.

Note that the IsElementaryAbelian sets and tests G.isElementaryAbelian.

    gap> z4 := Group( (1,2,3,4) );;
    gap> IsElementaryAbelian( z4 );
    false
    gap> v4 := Group( (1,2)(3,4), (1,3)(2,4) );;
    gap> IsElementaryAbelian( v4 );
    true 

The default function GroupOps.IsElementaryAbelian returns true if G is abelian and for some prime p each generator is of order p.

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