Solvable groups with a given solvable length, and minimal composition length

Group extensions with special properties

“…Groups of given derived length and minimal composition length are known up to derived length 8, see [8]. Here we use the method from Section 6.3 to obtain new information on groups of derived length 10.…”

“…The group M has derived length 10 and composition length 24. It is conjectured that 24 is the minimal possible composition length for a group of derived length 10, see [8]. Previously the group M has been the only group known to achieve this bound.…”

“…In particular, we construct two new examples of groups of derived length 10 and composition length 24. It is conjectured that 24 is the minimal possible composition length for a group of derived length 10, see [8].…”

The derived series of a finite p-group

“…Glasby [9,10] studied soluble groups with a fixed derived length and smallest possible composition length.…”

The shape of solvable groups with odd order

“…(2,3,5)(4,6,7),(1,2,3,4,5,6,7) S and set H 3m = A 3 wr H m where A 3 has order 3 and degree 3. The bound γ 0 log 2 c 0S (d)+ 2 3 < d is a consequence of d(H m ) = 2r, d(H 3m ) = 2r + 1, c(H m ) = m − 1 3 , c(H 3m ) = 4mIt follows from γ log 2 c − 2 3 < d and log 2 c 0 < d that c < 9 (d+1)/5 and c 0 < 2 d .…”