Zyklische Gruppe der Ordnung 11
gap> SmallGroupsInformation(11);
There is 1 group of order 11.
1 is of type c11.
The groups whose order factorises in at most 3 primes
have been classified by O. Hoelder. This classification is
used in the SmallGroups library.
This size belongs to layer 1 of the SmallGroups library.
IdSmallGroup is available for this size.
gap> c11 := CyclicGroup(11);
<pc group of size 11 with 1 generators>
gap> IsAbelian(c11);
true
gap> IsCyclic(c11);
true
gap> Elements(c11);
[ <identity> of ..., f1, f1^2, f1^3, f1^4, f1^5, f1^6, f1^7, f1^8, f1^9,
f1^10 ]
gap> List(c11, Order);
[ 1, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11 ]
gap> c11_Aut := AutomorphismGroup(c11);
<group with 1 generators>
gap> Elements(c11_Aut);
[ IdentityMapping( <pc group of size 11 with 1 generators> ),
[ f1 ] -> [ f1^2 ], Pcgs([ f1 ]) -> [ f1^3 ], Pcgs([ f1 ]) -> [ f1^4 ],
Pcgs([ f1 ]) -> [ f1^5 ], Pcgs([ f1 ]) -> [ f1^6 ],
Pcgs([ f1 ]) -> [ f1^7 ], Pcgs([ f1 ]) -> [ f1^8 ],
Pcgs([ f1 ]) -> [ f1^9 ], Pcgs([ f1 ]) -> [ f1^10 ] ]
gap> IsAbelian(c11_Aut);
true
gap> IsCyclic(c11_Aut);
true
gap> List(c11_Aut, Order);
[ 1, 10, 5, 5, 5, 10, 10, 10, 5, 2 ]