|A（G）|=2^t pqr（1≤t≤3）的有限Abel群G的构造

|A（G）|=2 t pqr（1≤t≤3）的有限Abel群G的构造 THE STRUCTURES OF FINITE ABELIAN GROOPS OF |A（G）|=2 t pqr （1≤t≤3） 黄本文 Huang Benwen 1 2 first-author 武汉大学数学系,武汉 武汉大学数学系,武汉 Depertment of Mathematics, Wuhan University Depertment of Mathematics, Wuhan University ,430072 ,430072 本文利用有限Abel群G的自同构群A（G）的阶来刻划群G的构造,证明了当|A（G）2 t pqr（1≤t≤3）时,G最多有207型。 We have discussed structures of Abelian group G by order |A（G）| of automorphism group and obtained all types of finite Abelian group G when the order of A（G） equals 2’pqr （1≤t≤3, p, q, r and different odd primes）. The following theorem is proved: Theorem Let G be finite A belian group, if|A（G）|=2’pqr （1≤t≤3, p, q, r are different odd primes）, then 1) G has 8’types when t=1, 2) G has 53 types when t=2, 3) G has 146 types when t=3. 自同构群 Abel群 群构造 Enler函数 automorphism group abelian group Structure of group Enler function O152.1 1993-02-01 2021-04-01 2