Abstract
In this paper, we compute the standard invariant of the 'subgroup-subfactor' P× α|H H⊂P× α G, where α denotes an outer action of a finite group G on a II 1 factor P, and P× α|H H denotes the obvi- ous crossed-product obtained by restricting the action to H. We then use this description to exhibit a pair of non-isomorphic subgroups H i , i=1, 2, of the symmetric group S 4 such that the subfactors R× α|H i H i ⊂P× α G, i=1, 2 are conjugate, thereby disproving a conjecture of Thomsen-see [9]-that 'the subgroup-subfactor re- members the subgroup' (provided the subgroup contains no non-trivial normal subgroup of the ambient group).
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