[GAP Forum] Solvable Groups

[Charles Wright]

OOPS! Don't know what i was thinking.

Charley

On 1/1/20 8:57 PM, Charles Wright wrote:
> Dear Vince,
>
> It looks to me as if your groups are simply the solvable groups of odd 
> order.
>
> Subgroups of index 2 are normal, so you don't want any normal factor 
> groups that are 2-groups. In particular, the Frattini factor group 
> must have odd order. So the product of a 2-complement and the Frattini 
> group must be the whole thing. But then the 2-complement is the whole 
> group.
>
> Am I missing something?
>
> Charley
>
> On 1/1/20 3:03 PM, Vince Giambalvo wrote:
>> Dear Forum,
>> As the title says, I am trying to study finite solvable groups with 
>> some nice (for me) properties that do not seem to be in the database. 
>> I don’t quite know which solvable group library, and or if there is 
>> another way.  “Not a direct product”, does seem to be in the 
>> libraries, and in addition if would like the Sylow 2 subgroup to be 
>> elementary abelian, and the group to have no subgroup of index 2. 
>> Does anyone have a suggestion for speeding up the search.
>>
>> Thanks for your help.
>>   Vince Giambalvo
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>>
>
>
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