Equation 677 Database

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Magma 1bcb8dbf450d…

magma 1bcb8dbf450d
Size
595
Isomorphism class hash
1bcb8dbf450dcd90200972718c4d248ad5521ca0608eca6a8faecebd8de58d85
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 06:42:12
Display reorder
96,112,126,40,97,113,127,41,98,114,128,42,99,115,129,43,94,116,124,44,95,117,125,45,88,84,85,86,87,83,527,515,522,510,513,212,220,207,288,283,291,294,39,102,35,15,166,177,200,178,183,167,14,25,2,154,284,292,295,236,259,231,213,444,441,456,442,436,381,385,376,429,427,431,433,392,410,34,16,184,176,202,179,165,13,24,3,155,151,159,160,339,353,336,333,366,364,370,322,297,211,219,206,289,285,293,296,235,260,230,324,326,365,374,373,360,332,334,328,430,428,432,434,393,411,389,462,463,440,464,461,582,580,512,546,514,543,511,521,518,550,554,590,594,589,560,564,494,483,471,489,488,503,475,414,378,426,435,443,399,386,279,271,305,272,247,217,256,92,174,37,110,7,150,164,122,61,26,141,182,130,69,218,257,255,301,232,264,208,498,501,493,482,472,496,505,418,403,384,409,408,438,390,111,5,148,162,123,58,27,142,180,131,67,22,93,91,173,36,109,6,149,163,121,59,28,139,181,132,68,23,351,350,363,337,354,330,357,161,270,60,221,140,519,516,572,557,535,573,528,525,540,566,563,548,552,567,562,549,152,172,157,75,50,133,106,239,319,275,250,204,209,233,101,105,1,153,171,158,76,242,273,262,240,320,276,251,261,210,234,258,205,286,299,156,74,49,134,107,47,199,137,79,103,12,38,100,0,287,300,290,248,241,274,263,478,509,495,486,492,468,476,490,466,499,502,500,484,479,135,108,48,198,136,80,104,331,338,352,327,358,362,359,405,396,419,413,395,455,420,485,412,380,391,491,592,591,579,529,556,581,542,545,531,524,578,585,539,559,537,583,506,487,477,481,474,504,473,469,508,497,470,480,507,467,361,346,342,369,349,340,343,33,175,31,17,195,143,19,71,192,11,168,54,188,90,238,245,229,303,225,214,317,144,20,72,193,8,169,55,310,254,237,246,227,302,226,18,196,145,21,73,194,9,170,56,189,89,46,57,32,439,388,382,454,423,383,404,453,379,437,398,448,407,394,244,228,304,224,215,318,280,216,70,197,10,298,584,586,587,558,523,538,571,588,536,526,575,533,517,534,577,555,306,266,252,282,315,267,311,187,138,29,78,53,63,201,64,66,51,185,119,81,146,316,268,312,308,277,223,249,377,401,457,402,397,445,415,406,425,452,416,449,447,421,30,77,4,62,203,65,52,186,118,82,147,191,120,190,368,356,335,347,329,344,371,321,243,309,265,253,281,314,269,313,307,278,222,325,323,345,375,372,341,367,355,348,424,451,417,450,446,422,387,460,459,400,465,458,574,576,568,565,570,551,569,553,561,530,532,541,593,520,544,547 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#48c37621e3e3a8ddab36004ec035b0c0f35c9a7774308f646142e24d2289a7aa, M = the submagma generated by {0, 1} (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 06:42:18 · history