Talk:Socle (mathematics)
Latest comment: 12 years ago by Rschwieb in topic "minimal non-trivial normal subgroups"
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A discussion of socle series/socle layers would probably be desirable at some point. --172.188.53.88 15:24, 9 August 2007 (UTC)
"minimal non-trivial normal subgroups"
editThe definition of 'socle' depends on the phrase 'minimal non-trivial normal subgroups', which is not defined. The Abelian example given is some help, but does not explain enough. What is the minimal non-trivial normal subgroup of A4? Maproom (talk) 11:33, 5 March 2012 (UTC)
- The most reasonable interpretation of "minimal non-trivial normal subgroup of a group G" is a minimal element of the poset of normal subgroups, excluding 0 and G. A4 has exactly three normal subgroups, two of them being trivial. I'll see if I can make an adjustment to the text to address your comments above. Rschwieb (talk) 13:47, 5 March 2012 (UTC)