群的融合自由积的πn-Frattini子群和πc-Frattini子群

Acta mathematica scientia,Series A ›› 2013, Vol. 33 ›› Issue (1): 123-126.

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πnFrattini Subgroups and πcFrattini Subgroups of Amalgamated Free Products of Groups

ZHANG Zhi-Rang, DENG Li-Ping, HE Pei-Pei

College of Mathematics, Chengdu University of Information Technology, Chengdu 610225

Received:2011-06-13 Revised:2012-08-19 Online:2013-02-25 Published:2013-02-25
Supported by:
国家自然科学基金(11071229)资助

Azarian M K generalizes the theorem on Frattini subgroups of amalgamated free products of two subgroups proposed by Tang C Y to the case of the free product of any set of subgroups with amalgamated subgroup. We consider πnFrattini subgroups and πcFrattini subgroups of the free product of any set of subgroups with amalgmated subgroup being a cyclic group and obtain similar results.

Key words: πnFrattini subgroups, πcFrattini subgroups, Amalgamated free products of groups

CLC Number:

20D25

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ZHANG Zhi-Rang, DENG Li-Ping, HE Pei-Pei. πnFrattini Subgroups and πcFrattini Subgroups of Amalgamated Free Products of Groups[J].Acta mathematica scientia,Series A, 2013, 33(1): 123-126.

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References

[1] Tang C Y. On the Frattini subgroups of generalized free products with cyclic amalgamations. J Canad Math Bull, 1972, 15: 569--573

[2] Azarian M K. On the lower near Frattini subgroups of amalgamated free product of groups I. J Missouri Math Sci, 1990, 2: 105--144

[3] 郭钦, 张志让, 王英, 杨义先. 群的融合自由积的几种广义Frattini子群. 数学年刊, 2008. 29A(1): 67--70

[4] Zhang Z R, Han X. On two types of Frattini-like subgroups. Journal of Southwest University (Natural Science Edition), 2007, 29(10): 1--4

[5] Neumann B H. An essay on free products of groups with amalgamations. Philos Trans Roy Soc London Ser, 1954, 246(A): 503--554

[6] Robinson D J S. A Course in the Theory of Groups (2nd ed). New York: Springer Verlag, 1996

[7] Derk K, Hawkes T. Finite Soluble Groups. Berlin: Walter de Gruyter, 1992

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πnFrattini Subgroups and πcFrattini Subgroups of Amalgamated Free Products of Groups

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