Equation 677 Database

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Magma cdb966ffc1b3…

magma cdb966ffc1b3
Size
705
Isomorphism class hash
cdb966ffc1b358d2ee9824b101bf8e790340b3ab0ec6d6c119532f3f0e923d04
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 15:33:29
Display reorder
704,499,470,485,75,500,76,468,483,469,77,498,484,502,473,74,481,503,471,72,482,501,472,73,480,497,491,476,81,495,489,474,82,496,490,475,83,487,493,479,80,488,494,477,78,486,492,478,79,504,505,506,507,508,509,510,511,515,513,514,512,660,663,662,661,202,226,229,367,203,368,227,230,225,366,201,228,198,222,370,232,199,223,371,233,200,224,369,231,193,235,217,365,194,236,218,363,192,234,216,364,238,196,220,361,239,197,221,362,237,195,219,360,207,208,209,206,204,205,213,214,211,212,210,215,691,689,688,690,545,526,530,438,543,439,527,528,525,440,544,529,541,522,441,533,542,523,442,531,540,524,443,532,551,536,517,436,549,534,518,437,550,535,516,435,539,547,520,432,537,548,521,433,538,546,519,434,561,562,563,560,558,559,552,553,557,555,556,554,671,669,668,670,263,281,240,16,261,17,279,241,280,15,262,242,259,277,12,243,260,278,13,244,258,276,14,245,254,246,287,22,252,247,285,23,253,248,286,21,249,257,283,18,250,255,284,19,251,256,282,20,269,267,268,265,266,264,275,273,270,271,272,274,678,677,676,679,50,24,46,295,48,296,25,47,26,294,49,45,53,27,298,42,51,28,299,43,52,29,297,44,56,37,30,293,54,38,31,291,55,36,32,292,40,59,33,289,41,57,34,290,39,58,35,288,62,60,61,65,63,64,68,66,70,71,69,67,666,665,664,667,658,657,656,659,650,651,648,649,653,655,654,652,642,641,643,640,646,645,647,644,638,636,639,637,622,620,621,623,614,612,613,615,618,616,617,619,632,634,633,635,625,626,624,627,628,630,629,631,426,427,428,429,430,431,424,425,422,420,421,423,692,694,695,693,120,97,118,94,121,95,98,119,96,93,122,117,123,100,90,114,124,101,91,115,125,99,92,116,126,109,103,85,127,110,104,86,128,108,102,84,112,129,106,88,113,130,107,89,111,131,105,87,139,140,138,142,143,141,137,135,132,133,134,136,700,702,703,701,318,341,308,7,319,8,339,306,340,6,320,307,321,337,10,311,322,338,11,309,323,336,9,310,316,303,347,5,317,304,345,3,315,305,346,4,302,312,343,0,300,313,344,2,301,314,342,1,334,335,333,330,331,332,325,326,327,328,329,324,696,698,699,697,418,394,396,467,419,465,395,397,393,466,417,398,414,390,463,399,415,391,464,400,416,392,462,401,409,402,385,458,410,403,386,456,408,404,384,457,405,412,388,461,406,413,389,459,407,411,387,460,375,376,377,374,372,373,381,382,379,380,378,383,675,673,672,674,150,175,184,355,151,356,176,185,174,354,152,183,153,178,358,180,154,179,359,181,155,177,357,182,148,190,173,353,149,191,171,351,147,189,172,352,186,144,169,349,187,145,170,350,188,146,168,348,167,165,166,163,164,162,158,156,160,161,159,157,680,681,683,682,594,572,584,446,595,444,570,582,571,445,596,583,597,575,449,587,598,573,447,585,599,574,448,586,592,579,567,452,593,580,568,450,591,581,569,451,578,588,566,455,576,589,564,453,577,590,565,454,609,610,611,608,606,607,600,601,605,603,604,602,684,687,686,685 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#200706f015266953205238906f67170c94edeebe72a54762b43b1258f263dcc8, 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 15:33:30 · history