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edit approved Dec 10, 2018 at 14:19
Mikko Korhonen
edit approved Dec 10, 2018 at 14:19
Mikko Korhonen
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Here are a few more references:

  • S. Adnan, On groups having exactly $2$ conjugacy classes of maximal subgroups, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8) 66 (1979), no. 3, 175–178. link
  • S. Adnan, On groups having exactly $2$ conjugacy classes of maximal subgroups. II, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8) 68 (1980), no. 3, 179. link
  • W. Shi, Finite groups having at most two classes of maximal subgroups of the same order, Chinese Ann. Math. Ser. A 10 (1989), no. 5, 532–537.
  • V. A. Belonogov, Finite groups with three classes of maximal subgroups, Math. Sb. 131 (1968), 225–239. link
  • X. Li, Finite groups having three classes of maximal subgroups of the same order, Acta Math. Sinica 1 (1994), 108–115.
  • G. Pazderski, Über maximale Untergruppen endlicher Gruppen, Math. Nachr. 26 (1963/1964), 307–319.
  • J. Shi, W. Shi, and C. Zhang, The type of conjugacy classes of maximal subgroups and characterization of finite groups, Comm. Algebra 38 (2010), no. 1, 143–153. link
  • J. Wang, The number of maximal subgroups and their types, Pure Appl. Math. (Xi'an) 5 (1989), 24–33.

The main theorem of Belonogov's article states that

Theorem. A finite nonsolvable group has three conjugacy classes of maximal subgroups if and only if $G/\Phi(G)$ is isomorphic to $PSL(2,7)$ or $PSL(2,2^p)$ for some prime $p$.

Here are a few more references:

  • S. Adnan, On groups having exactly $2$ conjugacy classes of maximal subgroups, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8) 66 (1979), no. 3, 175–178.
  • S. Adnan, On groups having exactly $2$ conjugacy classes of maximal subgroups. II, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8) 68 (1980), no. 3, 179.
  • W. Shi, Finite groups having at most two classes of maximal subgroups of the same order, Chinese Ann. Math. Ser. A 10 (1989), no. 5, 532–537.
  • V. A. Belonogov, Finite groups with three classes of maximal subgroups, Math. Sb. 131 (1968), 225–239.
  • X. Li, Finite groups having three classes of maximal subgroups of the same order, Acta Math. Sinica 1 (1994), 108–115.
  • G. Pazderski, Über maximale Untergruppen endlicher Gruppen, Math. Nachr. 26 (1963/1964), 307–319.
  • J. Shi, W. Shi, and C. Zhang, The type of conjugacy classes of maximal subgroups and characterization of finite groups, Comm. Algebra 38 (2010), no. 1, 143–153.
  • J. Wang, The number of maximal subgroups and their types, Pure Appl. Math. (Xi'an) 5 (1989), 24–33.

The main theorem of Belonogov's article states that

Theorem. A finite nonsolvable group has three conjugacy classes of maximal subgroups if and only if $G/\Phi(G)$ is isomorphic to $PSL(2,7)$ or $PSL(2,2^p)$ for some prime $p$.

Here are a few more references:

  • S. Adnan, On groups having exactly $2$ conjugacy classes of maximal subgroups, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8) 66 (1979), no. 3, 175–178. link
  • S. Adnan, On groups having exactly $2$ conjugacy classes of maximal subgroups. II, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8) 68 (1980), no. 3, 179. link
  • W. Shi, Finite groups having at most two classes of maximal subgroups of the same order, Chinese Ann. Math. Ser. A 10 (1989), no. 5, 532–537.
  • V. A. Belonogov, Finite groups with three classes of maximal subgroups, Math. Sb. 131 (1968), 225–239. link
  • X. Li, Finite groups having three classes of maximal subgroups of the same order, Acta Math. Sinica 1 (1994), 108–115.
  • G. Pazderski, Über maximale Untergruppen endlicher Gruppen, Math. Nachr. 26 (1963/1964), 307–319.
  • J. Shi, W. Shi, and C. Zhang, The type of conjugacy classes of maximal subgroups and characterization of finite groups, Comm. Algebra 38 (2010), no. 1, 143–153. link
  • J. Wang, The number of maximal subgroups and their types, Pure Appl. Math. (Xi'an) 5 (1989), 24–33.

The main theorem of Belonogov's article states that

Theorem. A finite nonsolvable group has three conjugacy classes of maximal subgroups if and only if $G/\Phi(G)$ is isomorphic to $PSL(2,7)$ or $PSL(2,2^p)$ for some prime $p$.

added 243 characters in body
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M. Farrokhi D. G.
M. Farrokhi D. G.
  • 1.7k
  • 9
  • 13

Here are a few more references:

  • S. Adnan, On groups having exactly $2$ conjugacy classes of maximal subgroups, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8) 66 (1979), no. 3, 175–178.
  • S. Adnan, On groups having exactly $2$ conjugacy classes of maximal subgroups. II, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8) 68 (1980), no. 3, 179.
  • W. Shi, Finite groups having at most two classes of maximal subgroups of the same order, Chinese Ann. Math. Ser. A 10 (1989), no. 5, 532–537.
  • V. A. Belonogov, Finite groups with three classes of maximal subgroups, Math. Sb. 131 (1968), 225–239.
  • X. Li, Finite groups having three classes of maximal subgroups of the same order, Acta Math. Sinica 1 (1994), 108–115.
  • G. Pazderski, Über maximale Untergruppen endlicher Gruppen, Math. Nachr. 26 (1963/1964), 307–319.
  • J. Shi, W. Shi, and C. Zhang, The type of conjugacy classes of maximal subgroups and characterization of finite groups, Comm. Algebra 38 (2010), no. 1, 143–153.
  • J. Wang, The number of maximal subgroups and their types, Pure Appl. Math. (Xi'an) 5 (1989), 24–33.

The main theorem of Belonogov's article states that

Theorem. A finite nonsolvable group has three conjugacy classes of maximal subgroups if and only if $G/\Phi(G)$ is isomorphic to $PSL(2,7)$ or $PSL(2,2^p)$ for some prime $p$.

Here are a few more references:

  • S. Adnan, On groups having exactly $2$ conjugacy classes of maximal subgroups, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8) 66 (1979), no. 3, 175–178.
  • S. Adnan, On groups having exactly $2$ conjugacy classes of maximal subgroups. II, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8) 68 (1980), no. 3, 179.
  • W. Shi, Finite groups having at most two classes of maximal subgroups of the same order, Chinese Ann. Math. Ser. A 10 (1989), no. 5, 532–537.
  • V. A. Belonogov, Finite groups with three classes of maximal subgroups, Math. Sb. 131 (1968), 225–239.
  • X. Li, Finite groups having three classes of maximal subgroups of the same order, Acta Math. Sinica 1 (1994), 108–115.
  • G. Pazderski, Über maximale Untergruppen endlicher Gruppen, Math. Nachr. 26 (1963/1964), 307–319.
  • J. Shi, W. Shi, and C. Zhang, The type of conjugacy classes of maximal subgroups and characterization of finite groups, Comm. Algebra 38 (2010), no. 1, 143–153.
  • J. Wang, The number of maximal subgroups and their types, Pure Appl. Math. (Xi'an) 5 (1989), 24–33.

Here are a few more references:

  • S. Adnan, On groups having exactly $2$ conjugacy classes of maximal subgroups, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8) 66 (1979), no. 3, 175–178.
  • S. Adnan, On groups having exactly $2$ conjugacy classes of maximal subgroups. II, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8) 68 (1980), no. 3, 179.
  • W. Shi, Finite groups having at most two classes of maximal subgroups of the same order, Chinese Ann. Math. Ser. A 10 (1989), no. 5, 532–537.
  • V. A. Belonogov, Finite groups with three classes of maximal subgroups, Math. Sb. 131 (1968), 225–239.
  • X. Li, Finite groups having three classes of maximal subgroups of the same order, Acta Math. Sinica 1 (1994), 108–115.
  • G. Pazderski, Über maximale Untergruppen endlicher Gruppen, Math. Nachr. 26 (1963/1964), 307–319.
  • J. Shi, W. Shi, and C. Zhang, The type of conjugacy classes of maximal subgroups and characterization of finite groups, Comm. Algebra 38 (2010), no. 1, 143–153.
  • J. Wang, The number of maximal subgroups and their types, Pure Appl. Math. (Xi'an) 5 (1989), 24–33.

The main theorem of Belonogov's article states that

Theorem. A finite nonsolvable group has three conjugacy classes of maximal subgroups if and only if $G/\Phi(G)$ is isomorphic to $PSL(2,7)$ or $PSL(2,2^p)$ for some prime $p$.

Source Link
M. Farrokhi D. G.
M. Farrokhi D. G.
  • 1.7k
  • 9
  • 13

Here are a few more references:

  • S. Adnan, On groups having exactly $2$ conjugacy classes of maximal subgroups, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8) 66 (1979), no. 3, 175–178.
  • S. Adnan, On groups having exactly $2$ conjugacy classes of maximal subgroups. II, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8) 68 (1980), no. 3, 179.
  • W. Shi, Finite groups having at most two classes of maximal subgroups of the same order, Chinese Ann. Math. Ser. A 10 (1989), no. 5, 532–537.
  • V. A. Belonogov, Finite groups with three classes of maximal subgroups, Math. Sb. 131 (1968), 225–239.
  • X. Li, Finite groups having three classes of maximal subgroups of the same order, Acta Math. Sinica 1 (1994), 108–115.
  • G. Pazderski, Über maximale Untergruppen endlicher Gruppen, Math. Nachr. 26 (1963/1964), 307–319.
  • J. Shi, W. Shi, and C. Zhang, The type of conjugacy classes of maximal subgroups and characterization of finite groups, Comm. Algebra 38 (2010), no. 1, 143–153.
  • J. Wang, The number of maximal subgroups and their types, Pure Appl. Math. (Xi'an) 5 (1989), 24–33.