Equation 677 Database

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Magma c9c6235c0e85…

magma c9c6235c0e85
Size
705
Isomorphism class hash
c9c6235c0e85b1a4ba0998afb8ba874be3e62aefcbdb239dd25d77dfec540fbc
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 18:15:59
Display reorder
660,147,220,213,539,162,214,218,537,163,148,219,146,212,538,161,150,223,216,535,158,151,221,217,536,159,149,222,215,534,160,226,153,211,545,168,224,154,209,543,169,225,152,210,544,167,156,229,207,541,164,157,227,208,542,165,540,155,228,206,166,686,677,675,681,62,272,508,410,441,506,273,408,439,63,274,64,507,409,440,65,275,504,406,437,66,276,505,407,438,67,277,503,405,436,270,60,514,416,447,271,61,512,414,445,269,59,513,415,446,56,266,510,412,443,57,267,511,413,444,411,58,268,509,442,667,669,664,663,234,171,398,496,253,396,172,494,251,235,170,233,397,495,252,230,174,394,492,249,231,175,395,493,250,232,173,393,491,248,177,240,404,502,244,178,241,402,500,242,176,239,403,501,243,236,180,400,498,247,237,181,401,499,245,497,238,179,399,246,676,674,682,680,106,114,419,390,532,417,115,391,530,104,113,105,418,392,531,109,110,422,389,528,107,111,420,387,529,108,112,421,388,527,120,655,654,652,657,121,639,638,636,641,119,647,646,644,649,621,116,620,624,625,631,117,630,628,633,386,43,118,423,533,703,699,704,697,304,82,453,293,429,451,80,294,427,302,81,303,452,295,428,307,85,449,292,425,305,83,450,290,426,306,84,448,291,424,88,310,459,299,435,86,308,457,300,433,87,309,458,301,434,313,91,455,298,431,311,89,456,296,432,297,312,90,454,430,692,689,691,690,465,2,575,186,484,573,1,187,482,463,0,464,574,185,483,461,5,571,182,480,462,3,572,183,481,460,4,570,184,479,8,471,581,192,490,6,469,579,193,488,7,470,580,191,489,467,11,577,188,486,468,9,578,189,487,190,466,10,576,485,671,665,666,668,520,99,356,75,132,357,100,76,133,518,98,519,358,74,131,516,102,359,78,128,517,103,360,79,129,515,101,361,77,130,97,526,354,73,123,95,524,355,71,124,96,525,353,72,122,522,93,350,69,126,523,94,351,70,127,68,521,92,352,125,695,693,696,694,613,34,594,142,367,592,35,140,365,611,33,612,593,141,366,609,30,590,145,363,610,31,591,143,364,608,32,589,144,362,25,619,600,137,373,26,617,598,138,371,24,618,599,139,372,615,28,596,136,369,616,29,597,134,370,135,614,27,595,368,685,688,673,679,587,13,41,606,477,42,14,604,475,585,12,586,40,605,476,583,16,37,602,473,584,17,38,603,474,582,15,39,601,472,19,658,653,659,656,20,642,637,643,640,18,650,645,651,648,627,22,626,623,622,634,23,629,635,632,607,588,21,36,478,698,701,700,702,551,55,256,379,278,254,53,377,279,549,54,550,255,378,280,547,51,259,375,281,548,52,257,376,282,546,50,258,374,283,46,557,262,385,284,44,555,260,383,285,45,556,261,384,286,553,49,265,381,287,554,47,263,382,288,380,552,48,264,289,661,670,672,662,321,197,342,563,327,343,198,561,328,322,199,320,341,562,326,324,196,338,559,330,325,194,339,560,331,323,195,340,558,329,203,319,348,569,333,204,317,349,567,334,205,318,347,568,332,315,202,344,565,336,316,200,345,566,337,564,314,201,346,335,684,678,687,683 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#70fbce4d1be954c5232f18b8807a18e39f88f6f161a168e0f82db887a05a7819, 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 18:16:03 · history