# Template:Finite p-group subgroup structure facts to check against

From Groupprops

Revision as of 17:53, 22 June 2011 by Vipul (talk | contribs) (Created page with "{{quotation|'''FACTS TO CHECK AGAINST FOR SUBGROUP STRUCTURE''': (group of prime power order)<br>Lagrange's theorem (order of subgroup times index of subgroup equals orde...")

FACTS TO CHECK AGAINST FOR SUBGROUP STRUCTURE: (group of prime power order)

Lagrange's theorem (order of subgroup times index of subgroup equals order of whole group, so all subgroups have prime power orders)|order of quotient group divides order of group (and equals index of corresponding normal subgroup, so all quotients have prime power orders)

prime power order implies not centerless | prime power order implies nilpotent <nowiki>prime power order implies center is normality-large

size of conjugacy class of subgroups divides index of center