Geodesic
Groups with few self-centralizing subgroups which are not self-normalizing
Hassanzadeh, Mahmoud1 ; Mostaghim, Zohreh1
1 Iran University of Science & Technology, Tehran, Iran
Rendiconti del Seminario Matematico della Università di Padova, Tome 142 (2019), pp. 69-80 Cet article a éte moissonné depuis la source Numdam

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A self-normalizing subgroup is always self-centralizing, but the converse is not necessarily true. Given a finite group G, we denote by w(G) the number of all self-centralizing subgroups of G which are not self-normalizing. We observe that w(G)=0 if and only if G is abelian, and that if G is nonabelian nilpotent then w(G)≥3. We also prove that if w(G)≤20 then G is solvable. Finally, we provide structural information in the case when w(G)≤3.

Publié le :
DOI : 10.4171/RSMUP/30
Classification : 20, 00
Mots-clés : Self-centralizing subgroup, self-normalizing subgroup, minimal simple group, A-group

Hassanzadeh, Mahmoud 1 ; Mostaghim, Zohreh 1

1 Iran University of Science & Technology, Tehran, Iran 
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     author = {Hassanzadeh, Mahmoud and Mostaghim, Zohreh},
     title = {Groups with few self-centralizing subgroups which are not self-normalizing},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     pages = {69--80},
     year = {2019},
     publisher = {European Mathematical Society Publishing House},
     address = {Zuerich, Switzerland},
     volume = {142},
     doi = {10.4171/RSMUP/30},
     mrnumber = {4032804},
     zbl = {1468.20043},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/RSMUP/30/}
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Hassanzadeh, Mahmoud; Mostaghim, Zohreh. Groups with few self-centralizing subgroups which are not self-normalizing. Rendiconti del Seminario Matematico della Università di Padova, Tome 142 (2019), pp. 69-80. doi: 10.4171/RSMUP/30

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