Equation 677 Database

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Magma ca0d52c23e34…

magma ca0d52c23e34
Size
705
Isomorphism class hash
ca0d52c23e34d0f6b3323b9037023c97b95e1c6c513fd73ddf23c82fa85e2d8c
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 21:45:11
Display reorder
660,71,506,510,505,512,69,526,525,530,532,486,485,70,490,492,67,421,426,430,432,68,449,448,450,451,66,466,465,470,472,626,630,62,625,632,646,650,60,645,652,606,610,61,605,612,546,550,65,545,552,570,566,63,565,572,586,590,64,585,592,693,687,691,689,273,503,504,508,507,274,523,528,524,527,483,488,272,484,487,269,424,428,425,427,270,456,458,457,444,271,463,468,464,467,623,624,264,628,627,643,644,265,648,647,603,604,263,608,607,543,544,267,548,547,564,563,268,568,567,583,584,266,588,587,685,695,690,698,258,350,410,338,279,259,351,339,411,280,349,337,257,409,278,261,346,334,406,275,262,347,335,407,276,260,348,336,408,277,356,416,256,344,285,357,417,254,345,286,355,415,255,343,284,352,412,252,340,281,413,353,253,341,282,354,414,251,342,283,680,667,662,668,134,159,113,314,326,132,160,315,111,327,161,313,133,112,325,137,158,310,109,322,135,156,311,110,323,136,157,312,108,324,165,119,140,320,332,166,117,138,321,333,167,118,139,319,331,164,115,143,316,328,116,162,141,317,329,163,114,142,318,330,665,663,664,675,239,502,515,511,509,240,522,531,535,529,482,491,241,495,489,242,423,431,435,429,243,443,446,447,445,244,462,471,475,469,622,635,245,631,629,642,655,246,651,649,602,615,247,611,609,542,557,248,551,549,577,562,249,571,569,582,597,250,591,589,700,694,703,692,73,519,518,517,513,74,539,537,538,533,499,497,72,498,493,76,439,437,438,433,77,442,440,441,452,75,479,478,477,473,639,637,79,638,633,657,659,80,658,653,619,617,78,618,613,559,556,82,555,553,576,579,83,575,573,599,596,81,595,593,699,704,697,688,56,500,514,501,516,54,520,521,534,536,480,481,55,494,496,59,422,420,434,436,57,455,454,459,453,58,461,460,474,476,620,634,51,621,636,641,654,52,640,656,600,614,53,601,616,541,554,50,540,558,574,561,48,560,578,580,594,49,581,598,686,702,701,696,97,126,5,307,294,98,127,308,3,295,128,309,96,4,293,100,129,306,0,297,101,130,304,2,298,99,131,305,1,296,124,11,103,299,292,125,9,104,419,290,123,10,102,300,291,120,7,106,301,288,8,121,107,302,289,122,6,105,303,287,683,682,671,672,12,88,374,155,362,13,89,153,375,363,87,154,14,373,361,15,84,151,370,358,16,85,152,371,359,17,86,150,372,360,94,380,18,146,368,95,381,19,144,369,93,379,20,145,367,90,376,21,149,364,377,91,22,147,365,92,378,23,148,366,676,670,673,684,178,386,212,28,398,179,387,29,210,399,385,27,177,211,397,174,382,24,215,394,175,383,25,213,395,176,384,26,214,396,392,207,169,34,404,393,208,170,35,405,391,209,168,33,403,388,206,172,30,400,204,389,173,31,401,390,205,171,32,402,679,666,678,677,192,37,222,187,233,193,38,188,223,234,36,186,194,224,235,195,40,190,225,236,196,41,191,226,237,197,39,189,227,238,43,220,198,185,228,44,221,199,183,418,42,219,200,184,229,46,216,201,181,230,217,47,202,182,231,45,218,203,180,232,669,661,681,674 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#9878faa9b07066f62fc077f7c99df5b1f6f079c61c0cd7e7f5bbdb9bc181adbc. 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 21:45:12 · history