(2, 3, k)-generated groups of large rank by Lucchini A.

By Lucchini A.

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The subgroups group. , and c o r r e s p o n d i n g K inequiwith M r , underlying matrix represen- ~r. Then each irreducible K-representation of G* is of the form F* := F I with representation M* := M I The u n d e r l y i n g ~... ~ F n =: ~ Fi, i where Vi ~... ~ M n =: vector denotes IF I Fr I module ~ Mi, i space where M i := M j, if is V* := V I @ K ' ' ' ~ where Fi the u n d e r l y i n g vector Vn =: | Vi ' i space of M i. F i = F J. 27 If nj denotes the number of factors equal to Fj 9 for Fi of F*, which are Sn( ~ H) consisting 1 < j < r, then m TF* := (n I .....

It is in fact known have character field for these presentations inequivalent tables over (cs I would like to show this directly system of pairwise S2~Snn A2 that Weyl Z, even that Curtis/Benson by constructing and irreducible may [I]). a complete ordinary re- of these groups. For this we need only construct tions of selfassociated with the normal subgroup the two irreducible the constituents representations of of the restric- $2~S n. 27 (alp) ~ S2~An, can be o b t a i n e d sentations where a = a' as r e p r e s e n t a t i o n s induced of a suitable subgroup To do this we first a p p l y in order to c o n s t r u c t representations.

These results together with the results of section conjugacy classes of ter table of S2%A n S2~A n 1 about the allow the evaluation of the charac- (which in general contains complex numbers). What can be said about the characters of $2~S n ? A2 It is known, that their values are rational integral. like to derive this)using the above results. 39 (ala) ~ S2~SnA 2 say as representations induced by certain representations of suitable subgroups. 40 $2" 0 S2~SnA 2 = {(f;ISn ) I ~ f ( i ) i = IS2} _< $2~S hA2.

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