Congruences between word length statistics for the finitary alternating and symmetric groups
نویسندگان
چکیده
منابع مشابه
homogenous finitary symmetric groups
we characterize strictly diagonal type of embeddings offinitary symmetric groups in terms of cardinality and the characteristic. namely, we prove thefollowing.let $kappa$ be an infinite cardinal. if$g=underset{i=1}{stackrel{infty}bigcup} g_i,$ where $ g_i=fsym(kappa n_i)$,$(h=underset{i=1}{stackrel{infty}bigcup}h_i, $ where $ h_i=alt(kappa n_i) ), $ is a group of strictly diagonal type and$xi=(...
متن کاملMaximal Ideals in Modular Group Algebras of the Finitary Symmetric and Alternating Groups
The main result of the paper is a description of the maximal ideals in the modular group algebras of the finitary symmetric and alternating groups (provided the characteristic p of the ground field is greater than 2). For the symmetric group there are exactly p − 1 such ideals and for the alternating group there are (p − 1)/2 of them. The description is obtained in terms of the annihilators of ...
متن کاملShort presentations for alternating and symmetric groups
We derive new families of presentations (by generators and relations) for the alternating and symmetric groups of finite degree n. These include presentations of length that are linear in log n, and 2-generator presentations with a bounded number of relations independent of n.
متن کاملCongruences for the Number of Spin Characters of the Double Covers of the Symmetric and Alternating Groups
Let p be an odd prime. The bar partitions with sign and p-bar-core partitions with sign respectively label the spin characters and p-defect zero spin characters of the double cover of the symmetric group, and by restriction, those of the alternating group. The generating functions for these objects have been determined by J. Olsson. We study these functions from an arithmetic perspective, using...
متن کاملCongruences between Selmer groups ∗
The study of congruences between arithmetically interesting numbers has a long history and plays important roles in several areas of number theory. Examples of such congruences include the Kummer congruences between Bernoulli numbers and congruences between coefficients of modular forms. Many of these congruences could be interpreted as congruences between special values of L-functions of arith...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Archiv der Mathematik
سال: 2017
ISSN: 0003-889X,1420-8938
DOI: 10.1007/s00013-017-1058-8