Equation 677 Database

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Magma 3fa79b79965b…

magma 3fa79b79965b
Size
705
Isomorphism class hash
3fa79b79965baec253839b67d546585d147973080b22d85f694c570ed95b06c8
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 18:46:02
Display reorder
660,511,86,507,513,514,527,84,533,534,531,487,85,491,493,494,89,428,431,433,434,87,448,450,451,452,88,467,471,473,474,92,631,633,627,634,651,90,653,647,654,91,611,613,607,614,551,95,553,547,556,571,93,573,567,576,591,94,593,587,596,697,685,687,686,506,26,512,505,503,532,24,525,523,526,492,25,486,485,483,29,432,427,426,423,27,458,457,456,445,28,472,466,465,463,32,626,625,632,623,646,30,645,652,643,31,606,605,612,603,546,35,545,552,543,566,33,565,572,563,586,34,585,592,583,688,700,696,694,304,14,316,388,340,317,12,389,341,305,315,13,303,387,339,17,312,300,384,336,15,313,301,385,337,16,314,302,386,338,20,310,394,322,346,311,18,395,323,347,19,309,393,321,345,306,23,390,318,342,307,21,391,319,343,308,22,392,320,344,680,668,664,661,205,186,9,160,284,10,187,161,282,206,11,188,204,159,283,189,8,208,156,287,190,6,209,157,285,191,7,207,158,286,184,211,166,1,279,212,185,167,0,280,183,210,165,2,281,214,180,162,3,278,215,181,163,4,276,213,182,164,5,277,663,672,675,666,502,56,509,501,510,529,54,520,530,522,489,55,482,481,490,59,429,422,421,430,57,446,444,443,447,58,469,462,460,470,51,622,621,629,630,642,52,640,649,650,53,602,601,609,610,542,50,541,549,550,562,48,561,569,570,582,49,580,589,590,689,701,703,698,519,99,518,517,508,538,100,537,528,539,498,101,499,497,488,98,438,439,437,424,96,441,442,440,449,97,477,479,478,468,105,639,638,637,628,657,106,658,659,648,107,619,618,617,608,559,104,554,555,548,579,102,574,575,568,599,103,594,595,588,695,690,699,704,504,222,515,500,516,535,223,521,536,524,495,224,484,480,496,225,435,425,420,436,226,459,455,454,453,227,475,464,461,476,220,624,620,635,636,644,221,641,655,656,219,604,600,615,616,544,216,540,557,558,564,217,560,577,578,584,218,581,597,598,693,691,702,692,295,179,328,405,352,329,177,406,353,296,327,178,294,403,351,175,324,298,397,348,176,325,299,398,349,174,326,297,400,350,170,293,416,334,358,291,168,418,335,359,169,292,415,333,357,289,173,409,330,354,290,171,410,331,355,288,172,412,332,356,682,684,665,673,130,201,116,137,145,114,202,135,146,131,115,203,129,136,144,200,119,126,133,148,198,117,127,134,149,199,118,128,132,147,192,121,143,111,151,122,193,141,112,152,194,120,142,113,150,124,195,139,110,154,125,196,140,108,155,123,197,138,109,153,676,674,683,678,364,42,376,268,79,377,43,269,80,365,375,44,363,267,78,45,372,360,264,82,46,373,361,265,83,47,374,362,266,81,40,370,274,382,77,371,41,275,383,75,39,369,273,381,76,366,36,270,378,73,367,37,271,379,74,368,38,272,380,72,679,671,677,670,404,69,253,238,245,254,70,239,243,407,252,71,402,237,244,68,256,396,234,241,66,257,399,235,242,67,255,401,236,240,60,417,229,259,251,419,61,230,260,249,62,414,228,258,250,408,63,232,262,247,411,64,233,263,248,413,65,231,261,246,667,669,662,681 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#8513f42721191fc76047535e55730c0acbdcae75cecf1dd6e4636ed6d0c5727e, 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 18:46:03 · history