On Just Infinite Abstract and Profinite Groups

摘要: An infinite group G is called just if all non-trivial normal subgroups have finite index; profinite it merely required that closed index. Just groups arisen in a variety of contexts. The abstract having abelian are precisely the space whose point act rationally irreducibly on (see McCarthy [7]). Many arithmetic known to be modulo their centres; examples SLn (R) for n ≥ 3 and Sp2n 2, where R ring integers an algebraic number field [1]). Nottingham over \(\mathop \mathbb{F}\nolimits_p\) (described Chapter 6) pro-p Groups. Grigorchuk [3], [4] Gupta Sidki [5] introduced studied some finitely generated p-groups which trees, many, together with completions, infinite. Using Zorn’s Lemma easy see S either or group, then has quotient group. Therefore decide whether group-theoretic property implies finiteness, sometimes sufficient consider groups.