# Template:Arithmetic function value rank of abelian p-group

minimum size of generating set || {{{1}}} || groups with same order and minimum size of generating set
• "{{{" can not be assigned to a declared number type with value 1.
• "{{{" can not be assigned to a declared number type with value 2.
| groups with same prime-base logarithm of order and minimum size of generating set
• "{{{" can not be assigned to a declared number type with value 1.
• "{{{" can not be assigned to a declared number type with value 3.
| groups with same minimum size of generating set
"{{{" can not be assigned to a declared number type with value 1.
||

|-

| subgroup rank of a group || {{{1}}} || groups with same order and subgroup rank of a group
• "{{{" can not be assigned to a declared number type with value 1.
• "{{{" can not be assigned to a declared number type with value 2.
| groups with same prime-base logarithm of order and subgroup rank of a group
• "{{{" can not be assigned to a declared number type with value 1.
• "{{{" can not be assigned to a declared number type with value 3.
| groups with same subgroup rank of a group
"{{{" can not be assigned to a declared number type with value 1.
|| same as minimum size of generating set since it is an abelian group of prime power order

|-

| rank of a p-group || {{{1}}} || groups with same order and rank of a p-group
• "{{{" can not be assigned to a declared number type with value 1.
• "{{{" can not be assigned to a declared number type with value 2.
| groups with same prime-base logarithm of order and rank of a p-group
• "{{{" can not be assigned to a declared number type with value 1.
• "{{{" can not be assigned to a declared number type with value 3.
| groups with same rank of a p-group
"{{{" can not be assigned to a declared number type with value 1.
|| same as minimum size of generating set since it is an abelian group of prime power order

|-

| normal rank of a p-group || {{{1}}} || groups with same order and normal rank of a p-group
• "{{{" can not be assigned to a declared number type with value 1.
• "{{{" can not be assigned to a declared number type with value 2.
| groups with same prime-base logarithm of order and normal rank of a p-group
• "{{{" can not be assigned to a declared number type with value 1.
• "{{{" can not be assigned to a declared number type with value 3.
| groups with same normal rank of a p-group
"{{{" can not be assigned to a declared number type with value 1.
|| same as minimum size of generating set since it is an abelian group of prime power order

|-

| characteristic rank of a p-group || {{{1}}} || groups with same order and characteristic rank of a p-group
• "{{{" can not be assigned to a declared number type with value 1.
• "{{{" can not be assigned to a declared number type with value 2.
| groups with same prime-base logarithm of order and characteristic rank of a p-group
• "{{{" can not be assigned to a declared number type with value 1.
• "{{{" can not be assigned to a declared number type with value 3.
| groups with same characteristic rank of a p-group
"{{{" can not be assigned to a declared number type with value 1.
|| same as minimum size of generating set since it is an abelian group of prime power order