On Non-commuting Sets in Certain Finite p-Groups

• 作者: Heguo Liu Yulei Wang
• 来源期刊: 代数集刊:英文版
• 学科: 数学
• 关键词: 非交换 P群 有限P-群 中心扩张 阿贝尔群 子集 基数
• 年，卷（期）: 2015,（4）
• 页码范围: 555-560
• 页数: 6页
• 分类号: O151.21
• 语种: 中文

摘要

Let G be a group. A subset X of G is said to be non-commuting if xy ≠ yx for any x, y ∈ X with x ≠ y. If {X}≥ IYI for any other non-commuting set Y in G, then X is said to be a maximal non-commuting set. In this paper, the bound for the cardinality of a maximal non-commuting set in a finite p-group G is determined, where G is a non-abelian p-group given by a central extension as1 → Zp→ G →Zp *→ * Zp →1 and its derivedsubgroup has order p.