Sentence examples for groups of orders from inspiring English sources

These groups are isomorphic to the free product of two finite cyclic groups of orders 2 and q.

The Hecke group H ( λ q ) is the Fuchsian group of the first kind when λ = λ q or λ = 2, and H is the Fuchsian group of the second kind when λ > 2. In this study, we focus on the case λ = λ q, q ≥ 3. The Hecke group H ( λ q ) is isomorphic to the free product of two finite cyclic groups of orders 2 and q, and it has a presentation H ( λ q ) = 〈 T, S ∣ T 2 = S q = I 〉 ≅ C 2 ∗ C q, [2].

Next, we derive the reference priors for groups of ordering.

By the structures of groups of order 12, we have that any group of order 12 is not a 2-Frobenius group, a contradiction.

Thereby the existence of difference sets in 22 nonabelian groups of order 96 is proved.

In this paper, we give a recursive theorem that for all odd n>1 constructs Paley partial difference sets in certain groups of order n4 and 9n4.

By the structures of the groups of order six and twelve, one has that G ≅ S 3 or A 4, where S 3 is a symmetric group of degree three and A 4 is an alternating group of degree four.

For any prime (p), there exists a finitely presented soluble group G with centre ((C_p)^{ infty )}), an infinite direct sum of cyclic groups of order (p) (see [103], as well as [104, Lemma 4.14]).

The correspondence between a (96,20,4) symmetric design having regular automorphism group and a difference set with the same parameters has been used to obtain difference sets in groups of order 96.

According to Lagrange's theorem, finite groups of order p, a prime number, are necessarily cyclic (abelian) groups Zp.

Groups of order p2 can also be shown to be abelian, a statement which does not generalize to order p3, as the non-abelian group D4 of order 8 = 23 above shows.