Equation 677 Database

← all  ·  ← by size  ·  ← size 595

Magma 51cd07e98975…

magma 51cd07e98975
Size
595
Isomorphism class hash
51cd07e98975987884b4edcd5b28611f08f196713f93873d9235a38f447746e6
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 594) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-08 22:17:43
Display reorder
14,13,15,16,17,18,112,111,113,114,115,110,302,301,300,305,303,304,397,396,398,399,400,401,456,457,458,461,459,460,534,514,518,572,568,269,268,168,270,271,213,175,65,68,69,67,66,59,64,60,61,62,63,2,5,3,216,217,4,214,215,170,171,0,1,26,25,27,28,29,220,210,260,209,261,207,208,221,178,222,179,223,177,192,141,142,143,144,145,353,352,351,350,348,349,338,337,336,339,340,341,402,404,403,407,405,406,425,424,423,421,422,420,390,392,391,395,393,394,388,387,389,384,385,386,503,502,501,498,500,499,530,547,517,512,519,515,516,556,571,555,557,590,554,579,558,593,7,12,8,9,10,11,105,108,106,107,104,103,100,99,101,102,97,98,44,43,45,46,47,42,82,81,83,84,85,86,152,151,153,154,155,237,248,158,246,247,197,198,242,241,156,243,244,196,176,70,71,72,73,74,290,289,288,293,291,292,504,506,505,508,509,507,466,465,467,463,462,464,453,455,454,452,450,451,484,483,485,481,480,482,317,316,315,313,314,312,306,308,307,311,309,310,531,522,525,528,529,524,546,569,583,559,564,548,562,563,585,549,120,125,121,122,123,124,21,24,22,23,20,19,30,35,31,32,33,34,57,56,58,53,54,55,41,40,36,37,38,39,49,48,50,51,52,274,280,169,281,277,272,273,276,278,157,279,275,245,236,150,146,147,148,149,416,415,414,419,417,418,371,370,369,366,367,368,297,299,298,296,294,295,427,426,428,429,430,431,331,330,332,333,334,335,377,376,375,373,374,372,379,378,380,381,382,383,539,536,520,510,513,521,511,552,580,551,553,594,550,581,586,574,93,92,94,95,96,91,160,253,205,255,204,254,203,206,251,202,252,201,235,190,191,132,133,134,165,164,166,167,265,266,159,250,267,199,200,249,182,229,183,230,184,185,238,194,239,195,240,193,181,228,225,109,226,227,440,439,438,443,441,442,433,432,434,437,435,436,355,354,356,357,358,359,449,448,447,445,446,444,360,362,361,365,363,364,346,345,347,342,343,344,494,493,492,496,497,495,541,545,538,537,532,533,535,577,587,592,565,582,588,566,584,561,76,75,77,78,79,80,162,256,259,161,258,257,187,186,232,233,116,231,234,188,189,119,117,118,88,87,89,90,180,224,219,218,172,173,174,6,129,128,130,131,126,127,139,138,140,135,136,137,163,212,263,264,262,211,413,412,411,410,408,409,486,487,488,491,489,490,318,320,319,323,321,322,326,325,324,328,329,327,469,472,471,473,468,470,285,287,286,284,283,282,479,478,477,474,476,475,527,526,543,523,542,540,544,573,567,560,589,576,570,591,578,575 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 595 = 35 + 5*112, from a common submagma at infinity. C(E, M, k, B) adjoins a submagma M (m elements) of a model E to every group of a transversal design TD(k, g), g = |E| - m, so that every enlarged group is a copy of E and all of them share M; every block carries B, a model of order k in which x*x = x. Two elements of M multiply in M; an element of M or of group i with one of group i, in group i's copy of E; elements of different groups, in their block. It satisfies Equation 677 whenever E and B do. This magma is C(E, M, 5, B) with E = magma#3cc60f474fc5309f8bfdc916c4fdc0ad032cdecf3f770b83999110b499ecb4f1, M = the submagma generated by {24, 42} (35 elements) in E, B = magma#e549b5f8492c9b6b5ad530e3aa4f39c6e23d08645ebd1b36a3c2de2a5a23bac5. Labels: 0..m-1 are M, in increasing order of their labels in E; m + g*i + c (i < k, c < g) is point c of group i, which plays the c-th element of E outside M, in increasing order. A block's point in group i plays element i of B. TD(5, 112): MacNeish's product over GF(16) x GF(7); GF(16) = F_2[x]/(x^4 + x + 1); GF(p^r) = F_p[x]/(f) labels c_0 + c_1 x + ... as c_0 + c_1 p + ..., and point c of a group is the c-th element of the product in lexicographic order. Block (a, b), a and b in the product, meets group i in the point whose coordinate in each field is a + s_i b, s_i the element of that field labelled i, or b when the field has exactly i elements. Equation 255: satisfied. Idempotent elements: 85.

last edited by qawbecrdtey at 2026-10-08 22:17:44 · history