Equation 677 Database

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Magma 79c2f4c230e5…

magma 79c2f4c230e5
Size
705
Isomorphism class hash
79c2f4c230e5f2fcd2d1cf17a6ba67c91c221f5e6ae19b0e54d071866cfdd1cd
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 18:20:28
Display reorder
704,214,323,218,201,215,202,321,216,213,203,322,217,200,210,319,221,198,211,320,219,199,212,318,220,192,224,314,205,193,222,312,206,194,223,313,204,227,195,317,208,225,196,315,209,226,197,316,207,183,184,185,182,180,181,189,190,187,188,186,191,675,673,674,672,561,406,573,549,562,550,407,574,563,551,405,575,548,560,402,572,546,558,403,570,547,559,404,571,540,564,397,552,541,565,398,553,542,566,396,554,567,543,400,555,568,544,401,556,569,545,399,557,531,532,533,530,528,529,537,538,535,536,534,539,664,666,665,667,12,162,0,230,13,228,163,2,14,229,164,1,233,15,165,4,231,16,166,5,232,17,167,3,236,7,160,18,234,8,161,19,235,6,159,20,10,239,156,21,11,237,157,22,9,238,158,23,648,649,650,651,652,653,654,655,658,656,657,659,685,686,684,687,41,29,53,78,39,79,27,51,40,80,28,52,81,37,25,49,82,38,26,50,83,36,24,48,76,59,35,47,77,57,33,45,75,58,34,46,55,72,31,43,56,73,32,44,54,74,30,42,68,66,67,71,69,70,63,64,61,62,60,65,701,703,700,702,333,462,614,647,334,645,463,612,335,646,464,613,643,332,465,617,644,330,466,615,642,331,467,616,638,620,460,324,636,618,461,325,637,619,459,326,623,641,456,327,621,639,457,328,622,640,458,329,627,628,629,626,624,625,633,634,631,632,630,635,691,688,690,689,141,262,98,129,142,130,263,96,143,131,261,97,128,140,258,101,126,138,259,99,127,139,260,100,120,104,253,132,121,102,254,133,122,103,252,134,107,123,256,135,105,124,257,136,106,125,255,137,111,112,113,110,108,109,117,118,115,116,114,119,662,661,663,660,357,469,369,345,358,346,470,370,359,347,468,371,344,356,472,368,342,354,473,366,343,355,471,367,336,360,475,348,337,361,476,349,338,362,474,350,363,339,478,351,364,340,479,352,365,341,477,353,375,376,377,374,372,373,381,382,379,380,378,383,694,693,695,692,608,251,178,595,606,596,249,179,607,594,250,177,598,611,247,174,599,609,248,175,597,610,246,176,593,169,242,603,591,170,240,604,592,168,241,605,172,589,245,602,173,590,243,600,171,588,244,601,584,582,583,587,585,586,579,580,577,578,576,581,682,683,681,680,500,388,510,488,498,486,389,511,499,487,387,512,491,503,384,513,489,501,385,514,490,502,386,515,483,508,394,495,484,509,395,496,485,507,393,497,504,482,390,494,505,480,391,492,506,481,392,493,522,523,524,525,526,527,520,521,518,516,517,519,696,698,699,697,414,89,423,447,415,448,87,424,416,449,88,425,446,417,85,422,444,418,86,420,445,419,84,421,453,429,95,412,454,430,93,413,455,431,94,411,428,452,91,408,426,450,92,409,427,451,90,410,432,433,434,435,436,437,438,439,443,441,442,440,671,668,670,669,307,154,267,295,308,296,155,268,306,294,153,269,298,310,150,266,299,311,151,264,297,309,152,265,293,273,145,305,291,274,146,303,292,275,144,304,272,289,148,301,270,290,149,302,271,288,147,300,277,278,276,280,281,279,283,284,285,286,287,282,676,678,677,679 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#7b4d86832894383b0b7ce3dfc16e526670032b07fced110816f25e14f2157e1a, 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 18:20:29 · history