We show that if the principal p-block of a finite group G contains exactly 5 irreducible ordinary characters, then a Sylow p-subgroup of G has order 5, 7 or is isomorphic to one of the non-abelian 2-groups of order 8.
Principal blocks with 5 irreducible characters / Rizo N.; Schaeffer Fry A.A.; Vallejo C.. - In: JOURNAL OF ALGEBRA. - ISSN 0021-8693. - STAMPA. - 585:(2021), pp. 316-337. [10.1016/j.jalgebra.2021.06.009]
Principal blocks with 5 irreducible characters
Vallejo C.
2021
Abstract
We show that if the principal p-block of a finite group G contains exactly 5 irreducible ordinary characters, then a Sylow p-subgroup of G has order 5, 7 or is isomorphic to one of the non-abelian 2-groups of order 8.
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