Equation 677 Database

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Magma c5a82a843da7…

magma c5a82a843da7
Size
705
Isomorphism class hash
c5a82a843da720b77b0f48b16c5a92d48c235f57d7f590d8b0e1a8e003d60d74
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 15:12:57
Display reorder
660,109,350,258,515,412,110,348,259,513,410,111,260,514,411,349,346,112,257,511,408,347,113,255,512,409,345,114,256,510,407,107,356,521,249,418,108,354,519,250,416,251,106,355,520,417,352,103,517,252,414,353,104,518,253,415,351,105,516,254,413,682,677,678,675,267,39,17,296,273,268,37,18,294,274,269,16,295,275,38,42,270,13,292,276,40,271,14,293,277,41,272,15,291,278,265,34,287,23,279,266,35,285,24,280,22,264,36,286,281,33,261,290,19,282,31,262,288,20,283,32,263,289,21,284,668,670,672,663,298,472,226,546,314,299,470,227,544,312,297,225,545,313,471,468,301,229,542,310,469,302,230,543,311,467,300,228,541,309,304,478,552,232,320,305,476,550,233,318,231,303,477,551,319,474,307,548,235,316,475,308,549,236,317,473,306,547,234,315,684,673,687,680,220,405,123,129,615,221,403,121,127,613,219,122,128,614,404,401,223,126,132,618,402,224,124,130,616,400,222,125,131,617,654,656,652,118,659,638,640,636,119,643,120,646,648,644,651,623,622,620,117,624,632,630,629,115,635,406,218,133,116,619,702,701,703,699,436,338,78,484,8,434,336,76,482,9,435,77,483,7,337,334,432,74,480,11,335,433,75,481,12,333,431,73,479,10,442,344,490,69,6,440,342,488,67,4,68,441,343,489,5,340,438,486,72,2,341,439,487,70,3,339,437,485,71,0,693,689,692,690,534,386,217,148,248,532,384,215,146,246,533,216,147,247,385,382,530,213,151,244,383,531,214,149,245,381,529,212,150,243,540,392,154,208,239,538,390,152,206,237,207,539,391,153,238,388,536,157,211,242,389,537,155,209,240,387,535,156,210,241,661,665,667,662,83,187,51,171,424,84,185,49,172,422,82,50,170,423,186,183,79,54,174,420,184,80,52,175,421,182,81,53,173,419,89,193,177,46,430,90,191,178,47,428,48,88,192,176,429,189,85,180,45,426,190,86,181,43,427,188,87,179,44,425,695,691,696,694,200,374,140,358,582,201,372,141,359,580,202,142,357,581,373,370,203,143,361,578,371,204,144,362,579,369,205,145,360,577,198,380,364,138,588,199,378,365,139,586,137,197,379,363,587,376,194,367,134,584,377,195,368,135,585,375,196,366,136,583,683,686,674,676,397,493,93,527,27,398,491,91,525,25,399,92,526,26,492,496,396,96,523,30,494,394,94,524,28,495,395,95,522,29,655,657,658,99,653,639,641,642,97,637,98,647,649,650,645,626,625,627,102,621,633,631,634,100,628,497,393,528,101,1,704,698,697,700,322,570,64,448,594,323,568,65,446,592,321,66,447,593,569,566,325,63,444,590,567,326,61,445,591,565,324,62,443,589,328,576,454,55,600,329,574,452,56,598,57,327,575,453,599,572,331,450,58,596,573,332,451,59,597,571,330,449,60,595,664,671,666,669,558,503,159,606,460,556,501,160,604,458,557,158,605,459,502,499,554,162,602,456,500,555,163,603,457,498,553,161,601,455,564,509,612,165,466,562,507,610,166,464,164,563,508,611,465,505,560,608,168,462,506,561,609,169,463,504,559,607,167,461,688,679,685,681 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#0afaa5a95ac3a042540e79b2adb5184e36490c06a1d05440665a030a584e7e24, 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 15:12:58 · history