# transitive group

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Related to transitive group: Faithful Group Action

## transitive group

[′tran·səd·iv ‚grüp]
(mathematics)
A group of permutations of a finite set such that for any two elements in the set there exists an element of the group which takes one into the other.
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The following graph displays Complexity in terms of the size of the group [absolute value of G] for transitive Groups on up to 9 variables (and excluding the alternate and symmetric group of degree 9).
Transitive Groups of degree 5 Database [absoulte Index in Canonicals number Id.
Note that Lemma 4.4 holds for any function invariant under some transitive group. But unfortunately the proof of Lemma 4.2 does not generalizes for all functions closed under some transitive group action.
So if a Boolean function, f, that is invariant under some transitive group, has all minterms of size k and weight at least (or at most) k/c for some constant c then the sensitivity of the function is [OMEGA]([n.sup.1/3]) and bs(f) = O(s[(f).sup.2]).

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