Equation 677 Database

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Magma 5ca3c7335798…

magma 5ca3c7335798
Size
705
Isomorphism class hash
5ca3c7335798181c25f756b18ff539101122019086c98a13bb8f349bd738519e
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 21:55:15
Display reorder
660,132,288,135,8,200,286,9,133,136,201,287,7,131,134,199,128,11,291,138,196,129,12,289,139,197,130,10,290,137,198,283,123,141,20,206,284,124,142,22,207,285,122,140,18,205,126,282,144,13,202,127,280,145,14,203,125,281,143,17,204,674,681,675,682,405,109,90,334,63,107,335,403,91,61,108,336,404,89,62,401,337,105,86,66,402,338,106,87,64,400,339,104,88,65,100,411,96,332,58,98,409,97,333,59,99,410,95,331,60,407,103,92,328,57,408,101,93,329,55,406,102,94,330,56,666,672,663,667,121,381,491,348,302,379,346,119,489,303,380,347,120,490,301,117,351,377,487,298,118,349,378,488,299,116,350,376,486,300,387,112,497,343,293,385,110,495,344,294,386,111,496,345,292,115,383,493,342,296,113,384,494,340,297,114,382,492,341,295,673,685,687,679,147,25,69,42,615,26,40,148,67,613,27,41,149,68,614,150,38,28,72,618,151,39,29,70,616,152,37,30,71,617,653,654,652,33,659,637,638,636,31,643,645,646,644,32,651,622,621,620,36,624,630,628,629,34,635,146,24,73,35,619,704,697,700,699,539,357,393,218,515,355,219,537,391,513,356,217,538,392,514,535,214,353,389,511,536,215,354,390,512,534,216,352,388,510,363,545,399,209,521,361,543,397,210,519,362,544,398,208,520,541,359,395,212,517,542,360,396,213,518,540,358,394,211,516,690,693,694,692,479,321,306,260,441,319,261,477,304,439,320,259,478,305,440,475,256,317,309,437,476,257,318,307,438,474,258,316,308,436,327,485,312,266,447,325,483,310,267,445,326,484,311,265,446,481,323,315,262,443,482,324,313,263,444,480,322,314,264,442,662,664,665,669,243,369,4,154,226,367,155,241,5,227,368,153,242,6,228,239,157,365,3,229,240,158,366,0,230,238,156,364,2,231,375,234,15,160,224,373,232,16,161,225,374,233,1,159,223,237,371,21,163,220,235,372,23,164,221,236,370,19,162,222,691,689,696,695,429,460,253,192,413,458,190,427,254,414,459,191,428,255,412,425,195,456,252,416,426,193,457,250,417,424,194,455,251,415,466,435,244,187,419,464,433,245,188,420,465,434,246,189,418,431,462,247,186,422,432,463,248,184,423,430,461,249,185,421,677,683,676,678,548,180,472,172,453,181,173,546,470,451,182,171,547,471,452,551,175,179,468,449,549,176,177,469,450,550,174,178,467,448,655,658,657,170,656,639,642,641,168,640,647,650,649,169,648,627,625,626,166,623,634,631,633,167,632,552,183,473,165,454,698,701,703,702,570,527,83,47,594,525,48,568,84,592,526,46,569,85,593,566,43,523,82,590,567,44,524,80,591,565,45,522,81,589,533,576,74,53,600,531,574,75,54,598,532,575,76,52,599,572,529,77,49,596,573,530,78,50,597,571,528,79,51,595,668,671,670,661,558,582,606,272,503,580,273,556,604,501,581,271,557,605,502,554,268,578,602,499,555,269,579,603,500,553,270,577,601,498,588,564,612,278,509,586,562,610,279,507,587,563,611,277,508,560,584,608,274,505,561,585,609,275,506,559,583,607,276,504,686,680,684,688 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#fbd23cd98406f165f23d6b41307d902a92b7e2e110ccd89116da4983a4804a48, 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 21:55:15 · history