Fusion systems for groups of order 8 - Revision history

Vipul at 05:27, 20 May 2012

2012-05-20T05:27:48Z

← Older revision		Revision as of 05:27, 20 May 2012
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	\| [[elementary abelian group:E8]] \|\| 5 \|\| 1 \|\| 1 \|\| [[fusion systems for elementary abelian group:E8]]		\| [[elementary abelian group:E8]] \|\| 5 \|\| 1 \|\| 1 \|\| [[fusion systems for elementary abelian group:E8]]
	\|}		\|}

			{{quotation\|To view these in a broader perspective, see [[fusion systems for groups of prime-cube order]] <nowiki>\|</nowiki> [[fusion systems for groups of order 2^n]]}}

	==Information on number of saturated fusion systems==		==Information on number of saturated fusion systems==

Vipul: /* Information on number of saturated fusion systems */

2012-05-05T00:29:45Z

Information on number of saturated fusion systems

← Older revision		Revision as of 00:29, 5 May 2012
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	{\| class="sortable" border="1"		{\| class="sortable" border="1"
	! Group !! GAP ID second part !! Hall-Senior number !! [[Nilpotency class]] !! Number of saturated fusion systems (strict counting) !! Number of saturated fusion systems up to isomorphism !! Is the group [[resistant group of prime power order\|resistant]]? In other words, does the identity functor control strong fusion in ''every'' saturated fusion system? (Yes if abelian)		! Group !! GAP ID second part !! Hall-Senior number !! [[Nilpotency class]] !! Number of saturated fusion systems (strict counting) !! Number of saturated fusion systems up to isomorphism !! Is the group [[resistant group of prime power order\|resistant]]? In other words, does the identity functor control strong fusion in ''every'' saturated fusion system? (Yes if abelian) !! Is it a [[group of prime power order with no exotic fusion system]]?
	\|-		\|-
	\| [[cyclic group:Z8]] \|\| 1 \|\| 3 \|\| 1 \|\| 1 \|\| 1 \|\| Yes		\| [[cyclic group:Z8]] \|\| 1 \|\| 3 \|\| 1 \|\| 1 \|\| 1 \|\| Yes \|\| Yes
	\|-		\|-
	\| [[direct product of Z4 and Z2]] \|\| 2 \|\| 2 \|\| 1 \|\| 1 \|\| 1 \|\| Yes		\| [[direct product of Z4 and Z2]] \|\| 2 \|\| 2 \|\| 1 \|\| 1 \|\| 1 \|\| Yes \|\| Yes
	\|-		\|-
	\| [[dihedral group:D8]] \|\| 3 \|\| 4 \|\| 2 \|\| 4 \|\| 3 \|\| No		\| [[dihedral group:D8]] \|\| 3 \|\| 4 \|\| 2 \|\| 4 \|\| 3 \|\| No \|\| Yes
	\|-		\|-
	\| [[quaternion group]] \|\| 4 \|\| 5 \|\| 2 \|\| 2 \|\| 2 \|\| Yes		\| [[quaternion group]] \|\| 4 \|\| 5 \|\| 2 \|\| 2 \|\| 2 \|\| Yes \|\| Yes
	\|-		\|-
	\| [[elementary abelian group:E8]] \|\| 5 \|\| 1 \|\| 1 \|\| 45 \|\| 4 \|\| Yes		\| [[elementary abelian group:E8]] \|\| 5 \|\| 1 \|\| 1 \|\| 45 \|\| 4 \|\| Yes \|\| Yes
	\|-		\|-
	! Total (5 groups) !! -- !! -- !! -- !! 53 !! 11 !! 4 Yes, 1 No		! Total (5 groups) !! -- !! -- !! -- !! 53 !! 11 !! 4 Yes, 1 No !! All Yes
	\|}		\|}

Vipul: /* Information on number of saturated fusion systems */

2012-05-05T00:29:06Z

Information on number of saturated fusion systems

← Older revision		Revision as of 00:29, 5 May 2012
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	{\| class="sortable" border="1"		{\| class="sortable" border="1"
	! Group !! GAP ID second part !! Hall-Senior number !! [[Nilpotency class]] !! Number of saturated fusion systems (strict counting) !! Number of saturated fusion systems up to isomorphism !! ~~Does~~ the identity functor control strong fusion in ''every'' saturated fusion system? (Yes if abelian)		! Group !! GAP ID second part !! Hall-Senior number !! [[Nilpotency class]] !! Number of saturated fusion systems (strict counting) !! Number of saturated fusion systems up to isomorphism !! Is the group [[resistant group of prime power order\|resistant]]? In other words, does the identity functor control strong fusion in ''every'' saturated fusion system? (Yes if abelian)
	\|-		\|-
	\| [[cyclic group:Z8]] \|\| 1 \|\| 3 \|\| 1 \|\| 1 \|\| 1 \|\| Yes		\| [[cyclic group:Z8]] \|\| 1 \|\| 3 \|\| 1 \|\| 1 \|\| 1 \|\| Yes

Vipul at 23:48, 4 May 2012

2012-05-04T23:48:50Z

← Older revision		Revision as of 23:48, 4 May 2012
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	\|}		\|}

	==Information on number of fusion systems==		==Information on number of saturated fusion systems==

	{{fusion systems facts to check against}}		{{fusion systems facts to check against}}

	{\| class="sortable" border="1"		{\| class="sortable" border="1"
	! Group !! GAP ID second part !! Hall-Senior number !! [[Nilpotency class]] !! Number of fusion systems (strict counting) !! Number of fusion systems up to isomorphism !! Does the identity functor control strong fusion? (Yes if abelian)		! Group !! GAP ID second part !! Hall-Senior number !! [[Nilpotency class]] !! Number of saturated fusion systems (strict counting) !! Number of saturated fusion systems up to isomorphism !! Does the identity functor control strong fusion in ''every'' saturated fusion system? (Yes if abelian)
	\|-		\|-
	\| [[cyclic group:Z8]] \|\| 1 \|\| 3 \|\| 1 \|\| 1 \|\| 1 \|\| Yes		\| [[cyclic group:Z8]] \|\| 1 \|\| 3 \|\| 1 \|\| 1 \|\| 1 \|\| Yes

Vipul at 23:48, 4 May 2012

2012-05-04T23:48:17Z

@@ Line 16: / Line 16: @@
 |-
 | [[elementary abelian group:E8]] || 5 || 1 || 1 || [[fusion systems for elementary abelian group:E8]]
 |}

Vipul at 16:15, 26 April 2012

2012-04-26T16:15:45Z

← Older revision		Revision as of 16:15, 26 April 2012
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	information type = fusion systems\|		information type = fusion systems\|
	connective = for}}		connective = for}}

			{\| class="sortable" border="1"
			! Group !! GAP ID second part !! Hall-Senior number !! [[Nilpotency class]] !! Fusion systems page
			\|-
			\| [[cyclic group:Z8]] \|\| 1 \|\| 3 \|\| 1 \|\| [[fusion systems for cyclic group:Z8]]
			\|-
			\| [[direct product of Z4 and Z2]] \|\| 2 \|\| 2 \|\| 1 \|\| [[fusion systems for direct product of Z4 and Z2]]
			\|-
			\| [[dihedral group:D8]] \|\| 3 \|\| 4 \|\| 2 \|\| [[fusion systems for dihedral group:D8]]
			\|-
			\| [[quaternion group]] \|\| 4 \|\| 5 \|\| 2 \|\| [[fusion systems for quaternion group]]
			\|-
			\| [[elementary abelian group:E8]] \|\| 5 \|\| 1 \|\| 1 \|\| [[fusion systems for elementary abelian group:E8]]
			\|}

Vipul: Created page with "{{all given order groups-specific information| order = 8| information type = fusion systems| connective = for}}"

2012-04-26T16:09:58Z

Created page with "{{all given order groups-specific information| order = 8| information type = fusion systems| connective = for}}"

New page

{{all given order groups-specific information|
order = 8|
information type = fusion systems|
connective = for}}