Automorphisms of nilpotent groups of class two with small rank
نویسندگان
چکیده
منابع مشابه
Amalgams of Nilpotent Groups of Class Two
In this paper we will prove analogues of B. Maier’s characterization of weak and strong embeddability of amalgams in N2 [12, 13] for the subvarieties of N2. We will also give analogues of D. Saracino’s characterization of weak and strong amalgamation bases [17], the author’s work on dominions [11] and on amalgamation bases in some varieties of nil-2 groups [8, 9]. Definitions will be recalled b...
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Now assume |G : H| is infinite and that H is definable in G (but H need no longer be infinite or G-normal). Let Z = Z◦(G), and note that (a) implies that Z is infinite. If |Z : H ∩Z| is infinite, then |HZ : H| is infinite as well. In this case we are done since H ≤ HZ ≤ NG(H). Otherwise, |Z : H ∩Z| is finite, so the connectedness of Z implies that Z ≤ H. We can now proceed by induction on the r...
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ژورنال
عنوان ژورنال: Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics
سال: 1985
ISSN: 0263-6115
DOI: 10.1017/s1446788700022230