Equation 677 Database

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Magma 03afcb8fa570…

magma 03afcb8fa570
Size
705
Isomorphism class hash
03afcb8fa57049c35b88b3dcb7a646cad9ded7466fc2e74cc4ee3d55be031d44
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 704) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-03 21:45:36
Display reorder
660,119,452,327,524,339,120,453,525,325,337,451,523,121,326,338,122,448,520,323,335,123,449,521,324,336,124,450,522,322,334,458,318,117,530,330,459,316,118,531,328,457,317,116,529,329,454,321,113,526,333,319,455,114,527,331,456,320,115,528,332,669,666,672,664,29,182,251,624,512,27,183,625,252,513,181,623,28,250,511,25,178,620,254,508,26,179,621,255,509,24,180,622,253,510,173,249,35,630,518,174,247,33,631,519,172,248,34,629,517,176,245,31,626,514,246,177,32,627,515,175,244,30,628,516,689,691,686,690,360,404,536,560,256,358,405,561,537,257,403,559,359,535,258,363,400,556,532,259,361,401,557,533,260,362,402,558,534,261,410,542,355,566,262,411,543,356,567,263,409,541,357,565,264,406,538,354,562,265,539,407,352,563,266,408,540,353,564,267,667,668,662,661,195,416,488,100,86,193,417,98,489,87,415,99,194,487,88,191,412,96,484,85,192,413,97,485,83,190,414,95,486,84,422,494,186,606,605,423,495,184,607,608,421,493,185,603,604,418,490,189,94,91,491,419,187,92,89,420,492,188,93,90,678,681,682,675,197,440,636,433,500,198,441,434,637,501,439,435,196,635,499,200,436,432,632,496,201,437,430,633,497,199,438,431,634,498,446,642,203,424,506,447,643,204,425,507,445,641,202,426,505,442,638,206,427,502,639,443,207,428,503,444,640,205,429,504,671,670,665,663,342,6,548,399,476,340,7,397,549,477,8,398,341,547,475,345,9,395,544,472,343,10,396,545,473,344,11,394,546,474,4,554,348,390,482,5,555,346,388,483,3,553,347,389,481,1,550,351,393,478,551,0,349,391,479,2,552,350,392,480,699,698,694,693,42,143,572,78,613,43,144,79,573,614,142,77,44,571,612,45,146,81,568,609,46,147,82,569,610,47,145,80,570,611,141,578,40,76,619,659,656,41,657,658,140,577,39,75,618,137,574,36,72,615,575,138,37,73,616,139,576,38,74,617,701,703,704,702,150,225,216,583,58,148,223,584,214,59,224,582,149,215,57,153,221,579,219,54,151,222,580,217,55,152,220,581,218,56,231,211,156,589,49,229,212,154,590,50,230,213,155,588,48,227,210,159,585,52,208,228,157,586,53,226,209,158,587,51,696,697,695,700,309,129,111,380,595,307,130,381,112,596,128,379,308,110,594,305,125,376,107,591,306,126,377,108,592,304,127,378,109,593,135,102,315,386,601,136,103,313,387,602,134,101,314,385,600,131,105,311,382,597,106,132,312,383,598,133,104,310,384,599,677,674,680,684,64,464,237,648,165,65,465,649,235,163,463,647,63,236,164,60,460,644,233,161,61,461,645,234,162,62,462,646,232,160,470,243,70,654,171,471,241,71,655,169,469,242,69,653,170,466,239,66,650,167,240,467,67,651,168,468,238,68,652,166,673,683,679,676,374,275,289,17,297,375,276,15,290,295,274,16,373,291,296,370,278,13,288,293,371,279,14,286,294,372,277,12,287,292,273,280,365,23,303,271,281,366,21,301,272,282,364,22,302,269,283,368,19,299,284,270,369,20,300,268,285,367,18,298,692,685,688,687 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 705 = 1 + 11*64, 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, 11, B) with E = magma#f1e2c600ebf06c2e31b8968226514217c5fc265d2577d787fe558118ce3f2b96, M = {60} in E, B = magma#ca58a4a9ddeee171fc40b5c556a5095e4a2c63eee13557dcdf190986f06d14c3. 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(11, 64): MacNeish's product over GF(64); GF(64) = F_2[x]/(x^6 + 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: 45.

last edited by qawbecrdtey at 2026-10-03 21:45:37 · history