Dear Gap Forum,

Igor Schein wrote:

misunderstanding by me or a serious problem. I examined
SmallGroup(16,1) through SmallGroup(16,14) using IsomorphicSubgroups,
and determined that that each group may contain TransitiveGroup(8,3)
or TransitiveGroup(8,5), among others, but never both. However, I can
present a degree-16 polynomial, whose Galois group is of size 16, and
which contains subfields with both Galois group TransitiveGroup(8,3)
and TransitiveGroup(8,5). If some1 can explain me how this is NOT a

Subfields correspond to factor groups, not subgroups and SmallGroup(16,13)
has two such factor groups.

Best regards,

Alexander Hulpke

Miles-Receive-Header: reply