Talk:Primitive permutation group
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The article defines a group to be primitive if it preserves no nontrivial partitions. In the last paragraph of the opening section, it is claimed that primitive permutation groups are transitive. A two element set has only trivial partitions. Therefore the action of the trivial group preserves no nontrivial partitions. However, this action is intransitive. So I think to get at common usage, transitivity needs to be built into the definition of primitivity. I'll try to reword the definition accordingly. Michael Kinyon (talk) 21:08, 7 December 2010 (UTC)
Primitive groups, degree 8
[edit]The table says there are 7 types of primitive groups of degree 8. Burnside (1911, pp. 218-221) seems to say there are 9. Additional groups with orders 96 and 192.
The 7 groups would be S8, A8, PGL(2,7), PSL(2,7), E(8):GL(3,2), E(8):7:3, E(8):7.
GL(3,2) has 2 sets (7 each) of subgroups isomorphic to S4. The 2 groups in question would have structures E(8):A4 and E(8):S4, the S4 group acting as S4 on an orbit of 4 and as S3 on an orbit of 3.
Would some kind soul add a section about insipid numbers?
[edit]Insipid numbers on OEIS https://oeis.org/A102842 — Preceding unsigned comment added by 83.29.28.131 (talk) 11:52, 2 October 2021 (UTC)