Growth series for the commutator subgroup

Concerning the Commutator Subgroup of a Ring

groups with minimax commutator subgroup

a result of dixon‎, ‎evans and smith shows that if $g$ is a locally (soluble-by-finite) group whose proper subgroups are (finite rank)-by-abelian‎, ‎then $g$ itself has this property‎, ‎i.e‎. ‎the commutator subgroup of $g$ has finite rank‎. ‎it is proved here that if $g$ is a locally (soluble-by-finite) group whose proper subgroups have minimax commutator subgroup‎, ‎then also the commutator s...

The Commutator Subgroup of a Group Generated by Two Operators.

in the San Gabriel and the San Gorgonio mountains about 40 and 90 miles to the east. But when it comes to matching the Glacial epochs of the coast with those of the Sierra Nevada as lately studied by Blackwelder,3 or of the northeastern United States, difficulty is encountered. A simple solution of the difficulty would be to equate the Budu coastal epoch with the next-to-last Glacial epoch, the...

Subgroup Series

If N is a nontrivial proper normal subgroup of a finite group G then N and G/N are smaller than G. While it is false that G can be completely reconstructed from knowledge of N and G/N (see Example 1.1 below), it is nevertheless a standard technique in finite group theory to prove theorems about finite groups by induction on the size of the group and thereby use information about the smaller gro...

Automorphism groups with cyclic commutator subgroup and Hamilton cycles

It has been shown that there is a Hamilton cycle in every connected Cayley graph on any group G whose commutator subgroup is cyclic of prime-power order. This note considers connected, vertex-transitive graphs X of order at least 3, such that the automorphism group of X contains a vertex-transitive subgroup G whose commutator subgroup is cyclic of prime-power order. We show that of these graphs...