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On Group-Characteristics

DOI: 10.1112/plms/s1-33.1.146
Source: OAI
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    ABSTRACT: A finite group G is partitioned into nonempty disjoint subsets C0, C1,…,Cm such that for every g1∈Ci the number of ordered pairs (g2,g3) for which g2∈Cν,g3∈Cj, and g1g2 = g3 is independent of the particular choice of g1. A sequence of mutually independent random elements γ0, γ1,…, γn,… is chosen in G in such a way that for n = 1,2,… the probability depends only on the class Cν which contains g. Let ξn = jif γ0γ1⋯γn∈Cj. Then is a homogeneous Markov chain with state space I = {0,1,…,m}. The aim of this paper is to determine the n-step transition probabilities of the Markov chain . The results derived in this paper lead also to a probabilistic interpretation and a generalization of group characters.
    Linear Algebra and its Applications 03/1982; 43:49–67. DOI:10.1016/0024-3795(82)90243-9 · 0.98 Impact Factor