Abelian quasinormal subgroups of groups

Stewart E. Stonehewer; Giovanni Zacher

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (2004)

  • Volume: 15, Issue: 2, page 69-79
  • ISSN: 1120-6330

Abstract

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Let G be any group and let A be an abelian quasinormal subgroup of G . If n is any positive integer, either odd or divisible by 4 , then we prove that the subgroup A n is also quasinormal in G .

How to cite

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Stonehewer, Stewart E., and Zacher, Giovanni. "Abelian quasinormal subgroups of groups." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 15.2 (2004): 69-79. <http://eudml.org/doc/252439>.

@article{Stonehewer2004,
abstract = {Let $G$ be any group and let $A$ be an abelian quasinormal subgroup of $G$. If $n$ is any positive integer, either odd or divisible by $4$, then we prove that the subgroup $A^\{n\}$ is also quasinormal in $G$.},
author = {Stonehewer, Stewart E., Zacher, Giovanni},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Quasinormal subgroup; Abelian groups; Abelian quasinormal subgroups; minimal quasinormal subgroups; products of subgroups; chains of quasinormal subgroups; finite -groups},
language = {eng},
month = {6},
number = {2},
pages = {69-79},
publisher = {Accademia Nazionale dei Lincei},
title = {Abelian quasinormal subgroups of groups},
url = {http://eudml.org/doc/252439},
volume = {15},
year = {2004},
}

TY - JOUR
AU - Stonehewer, Stewart E.
AU - Zacher, Giovanni
TI - Abelian quasinormal subgroups of groups
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 2004/6//
PB - Accademia Nazionale dei Lincei
VL - 15
IS - 2
SP - 69
EP - 79
AB - Let $G$ be any group and let $A$ be an abelian quasinormal subgroup of $G$. If $n$ is any positive integer, either odd or divisible by $4$, then we prove that the subgroup $A^{n}$ is also quasinormal in $G$.
LA - eng
KW - Quasinormal subgroup; Abelian groups; Abelian quasinormal subgroups; minimal quasinormal subgroups; products of subgroups; chains of quasinormal subgroups; finite -groups
UR - http://eudml.org/doc/252439
ER -

References

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  1. CURTIS, C.W. - REINER, I., Representation Theory of Finite Groups and Associative Algebras. Pure and Appl. Math., vol. 11, Interscience, New York1962. Zbl0131.25601MR144979
  2. GROSS, F., p -subgroups of core-free quasinormal subgroups. Rocky Mountain J. Math., 1, 1971, 541-550. Zbl0238.20040MR279192
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  6. ORE, O., On the application of structure theory to groups. Bull. Amer. Math. Soc., 44, 1938, 801-806. MR1563880JFM64.0054.04
  7. ROBINSON, D.J.S., A Course in the Theory of Groups. Graduate Texts in Math., 80, 2nd edition, Springer, New York1996. Zbl0836.20001MR1357169DOI10.1007/978-1-4419-8594-1
  8. SCHMIDT, R., Subgroup Lattices of Groups. Walter de Gruyter, Berlin1994. Zbl0843.20003MR1292462DOI10.1515/9783110868647
  9. SCOTT, W.R., Group Theory. Prentice-Hall, Inc., Englewood Cliffs, N.J.1964. Zbl0126.04504MR167513
  10. STONEHEWER, S.E., Permutable subgroups of infinite groups. Math. Z., 125, 1972, 1-16. Zbl0219.20021MR294510
  11. STONEHEWER, S.E., Permutable subgroups of some finite p -groups. J. Austral. Math. Soc., 16, 1973, 90-97. Zbl0279.20017MR332964

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