Sentence examples for minimal subgroup of from inspiring English sources

Let H / Φ ( N ) be a minimal subgroup of N / Φ ( N ).

If every minimal subgroup of F ( E ) is complemented in G, then G is supersoluble.

If every minimal subgroup of a group G of odd order is normal in G, then G is supersoluble.

Clearly, exp ( P / L ) = p. Let H / L be a minimal subgroup of P / L. Then H / L = 〈 x 〉 L / L for some x ∈ H ∖ L.

Then P is elementary abelian of exponent p. Let N be a minimal subgroup of P. Suppose that N has a supersoluble supplement T in G.

By the hypothesis and Lemma 2.1, every cyclic subgroup of L ∩ N with order 4 (if p=2) is weakly Φ-supplemented in L. Since every minimal subgroup of N of order p is contained in Z ( G ) and Z ( G ) ∩ L ≤ Z ( L ), every minimal subgroup of L ∩ N of order p is contained in Z ( L ).

Let ℱ be a saturated formation containing all supersoluble groups and G be a group with a normal soluble subgroup E such that G / E ∈ F. If all minimal subgroups of F ( E ∩ G ′ ) are complemented in G, then G ∈ F. Corollary 4.9 [19].

Let ℱ be a saturated formation containing all supersoluble groups and G be a group with a normal subgroup E such that G / E ∈ F. If every minimal subgroup and each cyclic subgroup with order 4 of F ∗ ( E ) is c-supplemented in G, then G ∈ F. Corollary 4.8 [18].

(2) P is a minimal parabolic subgroup of H.

Denote by (M_i) the unique minimal normal subgroup of (G_{i+1}).

P is a minimal parabolic subgroup of H.