Equation 677 Database

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Magma d57d10636ce1…

magma d57d10636ce1
Size
595
Isomorphism class hash
d57d10636ce1985d8f4b3d3c6127a0e29a86e591a5f1eed438353689706434df
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
2026-10-07 03:43:08
Display reorder
81,86,82,83,84,85,93,92,94,95,90,91,360,362,361,365,363,364,478,477,479,476,475,474,397,396,398,400,401,399,528,530,517,564,581,271,268,168,269,270,213,209,164,160,161,162,163,112,111,107,108,109,110,59,62,60,227,228,61,226,225,176,177,26,25,16,15,17,18,19,219,204,253,205,254,202,203,235,186,233,184,234,185,181,71,72,73,74,70,291,293,292,289,290,288,431,430,429,427,428,426,377,376,375,372,373,374,418,417,419,416,414,415,283,284,282,286,287,285,500,498,499,502,503,501,333,335,334,330,331,332,527,547,539,537,540,536,538,561,551,562,568,588,590,580,571,550,40,42,125,38,39,41,126,49,50,51,52,53,43,48,44,45,46,47,146,145,147,142,143,144,132,131,133,128,129,130,2,1,3,4,5,217,215,0,216,214,170,171,265,264,167,262,263,212,195,150,151,152,148,149,301,300,302,305,303,304,470,468,469,472,473,471,485,484,483,481,480,482,507,509,508,505,506,504,450,452,451,454,455,453,392,391,390,394,395,393,339,341,340,336,337,338,519,533,511,526,515,514,546,582,549,574,559,548,553,583,593,552,115,117,127,113,114,116,124,31,27,28,29,30,101,100,96,97,98,99,32,37,33,34,35,36,139,138,134,135,136,137,57,56,58,55,54,274,280,169,281,277,272,273,275,279,166,278,276,261,232,106,102,103,104,105,366,368,367,370,371,369,456,457,458,459,460,461,295,294,296,299,297,298,406,405,407,404,402,403,465,467,466,462,464,463,420,422,421,425,423,424,434,433,432,437,435,436,535,541,510,524,512,523,525,563,554,577,566,594,565,567,592,569,80,76,77,78,79,75,141,238,193,239,191,240,200,199,251,201,252,198,218,172,173,13,14,12,157,156,158,159,250,267,153,245,266,196,197,244,189,236,190,237,187,188,257,208,255,206,256,207,175,221,222,24,223,224,350,349,348,351,352,353,328,327,329,324,325,326,306,308,307,310,311,309,442,441,443,440,438,439,344,343,342,345,346,347,487,486,488,489,490,491,445,444,446,448,449,447,543,544,521,531,520,522,532,575,584,586,587,576,579,578,589,557,6,8,9,10,11,7,154,246,247,155,248,249,194,192,241,242,140,243,231,183,182,87,88,89,21,20,22,23,174,220,229,230,178,179,180,69,63,68,64,65,66,67,120,119,121,122,123,118,165,211,259,260,258,210,381,383,382,379,380,378,354,356,355,359,357,358,384,386,385,388,389,387,496,495,492,493,494,497,322,321,323,320,318,319,314,313,312,316,317,315,410,409,408,413,411,412,516,534,529,513,518,542,545,560,556,572,558,555,585,591,570,573 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#e4013d0178842fa1abe6ac84eb6d8732370ca50237187a2a953024cf339ab2c2, M = the submagma generated by {18, 30} (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 2026-10-07 03:43:14 · history