Template:Subgroup property implication in: Difference between revisions
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{{quotation| | {{quotation|This article gives the statement and possibly, proof, of an implication relation between two [[subgroup property|subgroup properties]], when the big group is a [[{{{group property}}}]]. That is, it states that in a [[Fact about::{{{group property}}}]], every subgroup satisfying the first subgroup property {{#if:{{{stronger|}}}|(i.e., [[Fact about::{{{stronger}}}]])}} must also satisfy the second subgroup property {{#if:{{{weaker|}}}|(i.e., [[Fact about::{{{weaker}}}]])}}. In other words, every {{#if:{{{stronger|}}}|[[Fact about::{{{stronger}}} of {{{group property}}};2| ]][[{{{stronger}}} of {{{group property}}}]]}} is a {{#if:{{{weaker|}}}|[[Fact about::{{{weaker}}} of {{{group property}}};3| ]][[{{{weaker}}} of {{{group property}}}]]}}.<br>[[:Category:Subgroup property implications in {{{group property}}}s|View all subgroup property implications in {{{group property}}}s]] <math>|</math> [[:Category:Subgroup property non-implications in {{{group property}}}s|View all subgroup property non-implications in {{{group property}}}s]] <math>|</math> [[:Category:Subgroup property implications|View all subgroup property implications]] <math>|</math> [[:Category:Subgroup property non-implications|View all subgroup property non-implications]]}}<includeonly>[[Category: Subgroup property implications]][[Category:Subgroup property implications in {{{group property}}}s]]</includeonly><noinclude>[[Category: Property implication specification templates]]</noinclude> | ||
Latest revision as of 17:07, 5 June 2015
This article gives the statement and possibly, proof, of an implication relation between two subgroup properties, when the big group is a [[{{{group property}}}]]. That is, it states that in a , every subgroup satisfying the first subgroup property must also satisfy the second subgroup property . In other words, every is a .
[[:Category:Subgroup property implications in {{{group property}}}s|View all subgroup property implications in {{{group property}}}s]] [[:Category:Subgroup property non-implications in {{{group property}}}s|View all subgroup property non-implications in {{{group property}}}s]] View all subgroup property implications View all subgroup property non-implications
