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Difference between revisions of "Thompson subgroup"

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The [[Characteristic subgroup|characteristic subgroup]] of a [[P-group|<img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/t/t092/t092700/t0927001.png" />-group]] generated by all Abelian subgroups of maximal order. Introduced by J.G. Thompson [[#References|[1]]].
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The [[characteristic subgroup]] of a [[P-group|$p$-group]] generated by all Abelian subgroups of maximal order. Introduced by J.G. Thompson [[#References|[1]]].
  
 
====References====
 
====References====
<table><TR><TD valign="top">[1]</TD> <TD valign="top">  J.G. Thompson,  "A replacement theorem for <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/t/t092/t092700/t0927002.png" />-groups and a conjecture"  ''J. Algebra'' , '''13'''  (1969)  pp. 149–151</TD></TR><TR><TD valign="top">[2]</TD> <TD valign="top">  D. Gorenstein,  "Finite groups" , Harper &amp; Row  (1968)</TD></TR></table>
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<TR><TD valign="top">[1]</TD> <TD valign="top">  J.G. Thompson,  "A replacement theorem for $p$-groups and a conjecture"  ''J. Algebra'' , '''13'''  (1969)  pp. 149–151 {{ZBL|0194.03902}}</TD></TR>
 
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<TR><TD valign="top">[2]</TD> <TD valign="top">  D. Gorenstein,  "Finite groups" , Harper &amp; Row  (1968) {{ZBL|0185.05701}}</TD></TR>
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====References====
 
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<table><TR><TD valign="top">[a1]</TD> <TD valign="top">  K. Doerk,  T. Hawkes,  "Finite soluble groups" , de Gruyter  (1992)  pp. 214</TD></TR></table>
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<table>
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<TR><TD valign="top">[a1]</TD> <TD valign="top">  K. Doerk,  T. Hawkes,  "Finite soluble groups" , de Gruyter  (1992)  pp. 214 {{ZBL|0753.20001}}</TD></TR>
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Revision as of 20:05, 22 October 2017

2020 Mathematics Subject Classification: Primary: 20D25 [MSN][ZBL]

The characteristic subgroup of a $p$-group generated by all Abelian subgroups of maximal order. Introduced by J.G. Thompson [1].

References

[1] J.G. Thompson, "A replacement theorem for $p$-groups and a conjecture" J. Algebra , 13 (1969) pp. 149–151 Zbl 0194.03902
[2] D. Gorenstein, "Finite groups" , Harper & Row (1968) Zbl 0185.05701

Comments

References

[a1] K. Doerk, T. Hawkes, "Finite soluble groups" , de Gruyter (1992) pp. 214 Zbl 0753.20001
How to Cite This Entry:
Thompson subgroup. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Thompson_subgroup&oldid=16050
This article was adapted from an original article by N.N. Vil'yams (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article