2-群中同谱但不同构的群的例子

本文找到了两个不同构的2(5)nn≥阶群G和H使得这两个群的各阶子群个数,各阶循环子群个数,各阶交换子群个数,各阶正规子群个数均相等。对徐明曜,曲海鹏在其《有限p群》一书中提出的问题12.1.12在2-群给出了一个否定回答。

In this paper we give two examples of 2-groups of non-isomorphism but isospetral. That is, there exist two non-isomorphism p-groups which have the same number of subgroups、cyclic subgroups、abelian subgroups and normal subgroups of each order, respectively.