query: Can all finite groups be distinguished either by their order, or by number of their subgroups?
positive_passages.docid: 152904
positive_passages.text: Groups with Same Number Of Elements and Subgroups
negative_passages.docid: 142228
negative_passages.text: Proof that a subset closed under group operation of a finite group is a subgroup
negative_passages.docid: 96878
negative_passages.text: A finite group with the property that all of its proper subgroups are abelian
negative_passages.docid: 13059
negative_passages.text: If a group is the union of two subgroups, is one subgroup the group itself?
negative_passages.docid: 56607
negative_passages.text: gcd and order of elements of group
negative_passages.docid: 31687
negative_passages.text: Classification of groups of order 30
negative_passages.docid: 81406
negative_passages.text: Does every set have a group structure?
negative_passages.docid: 116080
negative_passages.text: Let G be a finite group with more than one element. Show that G has an element of prime order
negative_passages.docid: 25835
negative_passages.text: Structure of groups of order $pq$, where $p,q$ are distinct primes.
negative_passages.docid: 155502
negative_passages.text: Index of a maximal subgroup in a finite group
negative_passages.docid: 8742
negative_passages.text: Examples and further results about the order of the product of two elements in a group
negative_passages.docid: 84789
negative_passages.text: Order of products of elements in a finite Abelian group
negative_passages.docid: 33152
negative_passages.text: Classifying groups of order 18
negative_passages.docid: 118849
negative_passages.text: If a cyclic group has an element of infinite order, how many elements of finite order does it have?
negative_passages.docid: 85379
negative_passages.text: Semigroup analogue to the classification of finite simple groups?
negative_passages.docid: 40846
negative_passages.text: When can a (finite) group be written as the quotient of some other group by its center?
negative_passages.docid: 113936
negative_passages.text: Showing that a finite abelian group has a subgroup of order m for each divisor m of n