Acta mathematica scientia,Series A ›› 2009, Vol. 29 ›› Issue (3): 737-740.
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Supported by:
国家自然科学基金(10671114)、山西省自然科学基金(2008012001) 和山西省回国留学人员基金（晋出留管办字 [2007]13-56)资助
Abstract:
In this note we classify finite p-groups in which any two noncommutative elements generate a subgroup of order p3. As a consequence, we solve the research problem No. 237 in [1]: Study the p-groups G such that |( x, y) | ≤ p3 for all x, y ∈ G.
Key words: p-groups, Metacyclic groups, Minimal non-abelian groups, 2-Engle condition
CLC Number:
ZHANG Qi-Hai, DENG Li-Jun, XU Ming-Yao. Finite p}-groups in which any Two Noncommutative Elements Generate a |Subgroup of Order p3[J].Acta mathematica scientia,Series A, 2009, 29(3): 737-740.
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URL: http://121.43.60.238/sxwlxbA/EN/
http://121.43.60.238/sxwlxbA/EN/Y2009/V29/I3/737
[1] Berkovich Y, Janko Z. Groups of Prime Power Order, Part 3. Berlin: Walter de Gruyter, 2004
[2] Huppert B. Endliche Gruppen I. New York: Springer-Verlag, 1967
[3] Daniel Gorenstein. Finite Groups. New York: Chelesa Publishing Company, 1980
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