A gap theorem for the ZL-amenability constant of a finite group
عنوان مقاله: A gap theorem for the ZL-amenability constant of a finite group
شناسه ملی مقاله: JR_THEGR-5-4_004
منتشر شده در در سال 1395
شناسه ملی مقاله: JR_THEGR-5-4_004
منتشر شده در در سال 1395
مشخصات نویسندگان مقاله:
Yemon Choi - Lancaster University
خلاصه مقاله:
Yemon Choi - Lancaster University
It was shown in [A. Azimifard, E. Samei and N. Spronk, Amenability properties of the centres of group algebras, J. Funct. Anal., ۲۵۶ no. ۵ (۲۰۰۹) ۱۵۴۴-۱۵۶۴.] that the ZL-amenability constant of a finite group is always at least ۱, with equality if and only if the group is abelian. It was also shown that for any finite non-abelian group this invariant is at least ۳۰۱/۳۰۰, but the proof relies crucially on a deep result of D. A. Rider on norms of central idempotents in group algebras. Here we show that if G is finite and non-abelian then its ZL-amenability constant is at least ۷/۴, which is known to be best possible. We avoid use of Rider's reslt, by analyzing the cases where G is just non-abelian, using calculations from [M. Alaghmandan, Y. Choi and E. Samei, ZL-amenability constants of finite groups with two character degrees, Canad. Math. Bull., ۵۷ (۲۰۱۴) ۴۴۹-۴۶۲.], and establishing a new estimate for groups with trivial centre.
کلمات کلیدی: Amenability constant, character degrees, just non-abelian groups
صفحه اختصاصی مقاله و دریافت فایل کامل: https://civilica.com/doc/1199629/