Re: [HM] technical term
Abe Shenitzer (shenitze@pascal.math.yorku.ca)
Wed, 3 Feb 1999 00:55:39 -0500 (EST)
The mystery is no more. G is metacyclic if it has a cyclic normal subgroup
C such that G/C is also cyclic.
Now consider S_5. This group contains a metacyclic subgroup with 20
elements. In turn, the latter contains a 10-element normal subgroup
isomorphic to the dihedral group D_5. The latter is referred to in the
Russian text as "semimetacyclic."
I mention this because Lagrange and Euler encountered these groups in
their work with equations.
(The "detective work" was done by my friend David Cox. One of his
colleagues suggested the simple explanation "semi"=half.)
Regards,
Abe (Shenitzer)
On Tue, 26 Jan 1999, Avinoam Mann wrote:
>
> On Sun, 24 Jan 1999, Abe Shenitzer wrote:
>
>> I came across the term "semimetacyclic" (about a group) in a Russian
>> historical text. What is the correct English term?
>>
>> Abe Shenitzer
>>
>
> Never heard that term (I am a group theorist). I think we have to know
> the meaning before giving a translation, because similar terms may mean
> different things in different languages. E.g. the term "metabelian group"
> has different meanings in the English and Russian literature, and it's
> possible that the same difference exists (or existed in the past) for
> metacyclic.
>
> Avinoam Mann