Let M≠ A10 be a simple K4-group. In this paper, we prove that if G is a finite group with the
same order and degree pattern as M, then G≅ M. Equivalently, all simple K4-groups except …

The degree pattern of a finite group G is introduced in [10] and it is proved that the following
simple groups are uniquely determined by their degree patterns and orders: all sporadic …

The degree pattern of a finite group G denoted by D (G) was introduced in [5]. We say that G
is k-fold OD-characterizable if there exist exactly k non-isomorphic finite groups having the …

Let G be a finite group and π (G) be the set of all prime divisors of its order. The prime graph
GK (G) of G is a simple graph with vertex set π (G), and two distinct primes p, q∈ π (G) are …

Let L2 (q) be the projective special linear group, where q is a prime power. In the present
paper, we prove that L2 (q) is OD-characterizable by using the classification of finite simple …

The degree pattern of a finite group M has been introduced by AR Moghaddamfar et
al.[Algebra Colloquium, 2005, 12 (3): 431–442]. A group M is called k-fold OD …

Let G be a finite group with order| G|= p 1 α 1 p 2 α 2… pk αk, where p 1< p 2<…< pk are
prime numbers. One of the well-known simple graphs associated with G is the prime graph …

Let M be a simple group whose order is less than 10 8. In this paper, we prove that if G is a
finite group with the same order and degree pattern as M, then the following statements …

The degree pattern of a finite group has been introduced in [18]. A group M is called k-fold
OD-characterizable if there exist exactly k non-isomorphic finite groups having the same …

Abstract top In the present paper, we classify groups with the same order and degree pattern
as an almost simple group related to the projective special linear simple group L 2 (49). As a …