Equation 677 Database

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Magma 422bb35727de…

magma 422bb35727de
Size
705
Isomorphism class hash
422bb35727ded240ca6942521951de1fee67b963e2c62e5ece41054d65b31e80
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 17:27:52
Display reorder
660,116,356,339,308,363,114,357,340,309,364,338,115,310,362,358,359,119,342,311,366,360,117,343,312,367,361,118,341,313,365,122,354,345,306,369,120,355,346,307,370,121,353,344,305,368,302,350,125,348,372,351,123,349,303,373,352,124,347,304,371,673,674,676,675,63,187,90,182,131,61,188,91,180,129,92,62,181,130,186,190,66,93,185,127,191,64,94,183,128,189,65,95,184,126,58,193,96,177,137,59,194,97,178,135,60,192,98,179,136,176,196,57,99,133,197,55,100,174,134,195,56,101,175,132,662,668,672,661,110,375,441,149,537,108,376,442,147,538,440,109,148,536,374,378,113,444,145,540,379,111,445,146,541,377,112,443,144,539,105,381,447,140,543,106,382,448,138,544,107,380,446,139,542,143,384,104,450,546,385,102,451,141,547,383,103,449,142,545,680,677,685,683,69,9,274,282,84,67,4,275,280,82,276,68,281,83,7,0,72,277,285,80,2,70,278,283,81,1,71,279,284,79,75,5,272,288,88,73,6,273,286,86,74,8,271,287,87,644,645,78,649,648,656,76,654,655,652,3,77,270,289,85,703,698,700,704,202,573,549,597,13,203,574,550,598,14,548,201,596,15,572,576,198,552,600,12,577,199,553,601,10,575,200,551,599,11,208,579,555,603,19,209,580,556,604,20,207,578,554,602,21,606,582,204,558,18,583,205,559,607,16,581,206,557,605,17,691,693,690,694,263,154,465,501,525,261,155,466,502,526,464,262,500,524,153,150,259,468,504,528,151,260,469,505,529,152,258,467,503,527,269,160,471,507,531,267,161,472,508,532,268,159,470,506,530,510,156,265,474,534,157,266,475,511,535,158,264,473,509,533,663,669,667,665,166,233,561,319,235,167,231,562,317,236,560,165,318,234,232,229,162,564,315,238,230,163,565,316,239,228,164,563,314,237,172,224,567,325,241,173,222,568,323,242,171,223,566,324,240,321,227,168,570,244,225,169,571,322,245,226,170,569,320,243,692,695,696,689,246,633,477,453,387,247,634,478,454,388,476,248,452,386,632,636,249,480,456,390,637,250,481,457,391,635,251,479,455,389,252,639,483,459,393,253,640,484,460,394,254,638,482,458,392,462,642,255,486,396,643,256,487,463,397,641,257,485,461,395,682,688,678,681,326,53,421,412,431,327,54,422,410,432,420,328,411,430,52,49,329,424,415,434,50,330,425,413,435,51,331,423,414,433,332,47,427,418,437,333,48,428,416,438,334,46,426,417,436,651,650,335,646,647,653,336,658,657,659,89,337,429,419,439,697,702,699,701,301,621,513,45,489,299,622,514,43,490,512,300,44,488,620,624,297,516,41,492,625,298,517,42,493,623,296,515,40,491,292,627,519,36,495,290,628,520,34,496,291,626,518,35,494,39,630,295,522,498,631,293,523,37,499,629,294,521,38,497,666,671,664,670,213,585,30,609,399,214,586,28,610,400,29,215,608,398,584,588,212,33,612,402,589,210,31,613,403,587,211,32,611,401,219,591,25,615,405,220,592,26,616,406,221,590,27,614,404,618,594,218,24,408,595,216,22,619,409,593,217,23,617,407,684,686,679,687 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#5779f8cee5daac7ffda88b67b379fba3aadfa70634d24364b86a2ac7cf85bc20, M = {60} in E, B = magma#abfd8e025ce71b705594dbbe1465dc1c7328d12d30e12d07906d7138f9d583bc. 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 17:27:54 · history