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''Hamiltonian group''

A non-Abelian group all subgroups of which are normal (cf. [[Normal subgroup|Normal subgroup]]). Such groups were studied by R. Dedekind and were named  "Hamiltonian groups"  by him after the creator of the algebra of quaternions, W.R. Hamilton. A non-Abelian group is Hamiltonian if and only if it is a direct product of the [[Quaternion group|quaternion group]] of order 8, an [[Abelian group|Abelian group]] each element of which is of finite odd order, and an Abelian group of exponent 1 or 2. In particular, any Hamiltonian group is periodic (cf. [[Periodic group|Periodic group]]).

====References====
<table><TR><TD valign="top">[1]</TD> <TD valign="top">  M. Hall,   "Group theory" , Macmillan  (1959)</TD></TR></table>



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====References====
<table><TR><TD valign="top">[a1]</TD> <TD valign="top">  B. Huppert,   "Endliche Gruppen" , '''1''' , Springer  (1967)</TD></TR></table>