Equation 677 Database

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Magma 0ccac10ebba5…

magma 0ccac10ebba5
Size
705
Isomorphism class hash
0ccac10ebba5ee61b84ae05318d98e2ac7d94d9574b9b301feac15ea6b981b6e
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 21:14:54
Display reorder
660,550,554,552,557,57,570,574,58,572,577,590,594,59,592,597,610,614,56,612,617,630,634,54,632,637,650,654,55,652,657,510,514,48,512,517,530,534,49,532,537,492,490,494,50,497,430,434,51,432,437,448,451,52,456,457,470,474,53,472,477,691,701,702,688,544,551,559,558,193,564,571,194,579,578,584,591,192,598,599,604,611,196,619,618,624,631,197,639,638,644,651,195,658,659,504,511,199,519,518,524,531,200,539,538,499,484,491,198,498,424,431,202,439,438,444,449,203,459,458,464,471,201,478,479,692,695,685,686,269,408,153,409,108,267,411,109,154,410,268,413,110,155,412,265,414,111,152,415,266,416,112,150,417,264,419,113,151,418,275,404,114,144,405,273,407,115,145,406,146,274,402,116,403,271,396,117,147,397,272,398,118,148,399,270,401,119,149,400,666,683,684,662,354,67,94,342,30,355,68,31,95,343,356,66,32,93,344,357,70,33,90,345,358,71,34,91,346,359,69,35,92,347,352,65,28,85,340,353,63,29,86,341,84,351,64,27,339,348,61,24,88,336,349,62,25,89,337,350,60,26,87,338,681,673,667,677,543,555,545,546,125,563,575,123,565,566,583,595,124,585,586,603,615,121,605,606,623,635,122,625,626,643,655,120,645,646,503,515,131,505,506,523,535,129,525,526,485,483,495,130,486,423,435,127,425,426,452,454,128,445,446,463,475,126,465,466,690,698,696,693,548,556,541,540,2,568,576,1,561,560,588,596,0,580,581,608,616,5,601,600,628,636,3,621,620,648,656,4,641,640,508,516,8,500,501,528,536,6,520,521,480,488,496,7,481,428,436,11,421,420,453,455,9,443,442,468,476,10,461,460,699,694,697,689,547,553,549,542,78,567,573,79,569,562,587,593,80,589,582,607,613,81,609,602,627,633,82,629,622,647,653,83,649,642,507,513,76,509,502,527,533,77,529,522,489,487,493,75,482,427,433,72,429,422,447,450,73,441,440,467,473,74,469,462,687,703,704,700,258,294,19,330,138,259,295,139,20,331,260,296,140,18,332,261,297,141,22,333,262,298,142,23,334,263,299,143,21,335,256,292,136,17,328,257,293,137,15,329,16,255,291,135,327,252,288,132,13,324,253,289,133,14,325,254,290,134,12,326,674,672,665,663,282,163,45,390,96,283,164,97,46,391,284,162,98,47,392,285,166,99,44,393,286,167,100,42,394,287,165,101,43,395,280,161,102,36,388,281,159,103,37,389,38,279,160,104,387,276,157,105,39,384,277,158,106,40,385,278,156,107,41,386,668,682,670,664,212,224,366,189,243,210,222,244,367,190,211,223,245,368,191,215,227,242,369,188,213,225,240,370,186,214,226,241,371,187,207,219,249,364,180,208,220,250,365,181,363,209,221,251,182,206,218,248,360,183,204,216,246,361,184,205,217,247,362,185,678,679,676,671,378,176,234,318,301,379,174,302,235,319,380,175,300,236,320,381,179,304,237,321,382,177,305,238,322,383,178,303,239,323,376,171,307,232,316,377,172,308,233,317,231,375,173,306,315,372,170,310,228,312,373,168,311,229,313,374,169,309,230,314,661,669,675,680 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#e0ddb86ffdf58ba66baf4adb67528755a1dfe5eefeff33f7cfcb062fa9d34ece, 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 21:14:54 · history