Sentence examples for m is isomorphic from inspiring English sources

Let M, M ′ ∈ A k. Open image in new window Then M is isomorphic to M′ if and only if there is a height-preserving isomorphism f:H k (M → Hk (M′).

A circulant graph with a jump relatively prime with m is isomorphic to a chordal ring.

D m is isomorphic to the dihedral group with 2m elements [7].

Since (M) is isomorphic to each cyclic submodules, (M) is cyclic and every submodule of (M) is cyclic and so (M) is noetherian.

First we remark that if a module (M) is isomorphic to all its non-zero submodules, then (M) must be uniform.

Obviously, E m is isomorphic to R m T and hence E m can be equipped with the inner product and norm ∥ ⋅ ∥ as ( u, v ) = ∑ j = 1 m T u j v j, u, v ∈ E m, and ∥ u ∥ = ( ∑ j = 1 m T u j 2 ) 1 2, u ∈ E m.

If | G | = | M 22 | and L ( G ) = L ( M 22 ), then either G is isomorphic to M 22 or H × M 11, where H is a Frobenius group with an elementary kernel of order 8 and a cyclic complement of order 7.

Now, suppose that m v n, w n ○…○ m v 0, w 0(G) is isomorphic to G′, by induction hypothesis, there exists an epimorphism ν from G to G′′ = m v n −1, w n −1 ○…○ m v 0, w 0(G).

Let us prove by induction on n that if m v n, w n ○…○ m v 0, w 0(G) is isomorphic to G′ then there exists an epimorphism from G to G′.

There exists an epimorphism μ from G to G′ if and only if there exists a finite sequence of merge operations, i.e. a finite sequence of pairs of vertices (v i, w i ) i ≤ n, such that the graph m v n, w n ○…○ m v 0, w 0(G) is isomorphic to G′.

If M = A 6, then G is isomorphic to one of the following groups: Aut ( A 6 ), Z 2 × Z 2 × A 6, Z 2 × ( Z 2 ⋅ A 6 ) and Z 4 × A 6. In other words, Aut ( A 6 ) is fourfold OD-characterizable.