Nonnormal subgroups of p-groups
Nonnormal subgroups of p-groups
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DOI：
10.1016/0021-8693(70)90064-5
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发表时间：
1970-07
影响因子：
0.9
通讯作者：
D. Passman
中科院分区：
文献类型：
--
作者：
D. Passman
设P是阶为p”的p-群。T1 xn，众所周知，P有一个正规子群，其每一个可能的阶p”，0“-”：a“-< II。本文研究了P的非正规子群的阶，当P有非正规子群时，引入以下符号是方便的。pmascP）= P的非正规子群的阶的最大值。pmin（P）= P的非正规子群的阶的最小值。V'e say H，：li，：. H_i是P的一个非正规子群链，如果每个Z_i，4 P，且如果/I_i，：i_I，2，…，k-~ I.这种链的长度是出现的基团的数量，使得上述链具有长度lz。chn（P）是P的非正规子群的链长的最大值。
Let P be a p-group of order p”. Tl xn, as is well-known, P has a normal subgroup of every possible order p” with 0 ‘-‘: a ‘-< II. In this paper we studythe orders of the nonnormal subgroups of P. It is convenient to introduce the following notation in case P has a nonnormal subgroup. pmascP)= the maximum of the orders of the nonnormal subgroups of P. pmin (P)= the minimum of the orders of the nonnormal subgroups of P.‘V\‘e say H,: li,:....’H,, is a chain of nonnormal subgroups of P if each Z1; 4 P and if/II,: fi, _,~~ p for i I, 2,..., k-~ I. The length of such a chain is the number of groups which occur so that the above chain has length lz. chn (P) the masimum of the lengths of the chains of nonnormal subgroups of P.