Equation 677 Database

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Magma 2be491a81498…

magma 2be491a81498
Size
705
Isomorphism class hash
2be491a8149897af2ea78184aea7ff72d4dd8e8c678c45aca41bdb0a056c6e53
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 18:16:16
Display reorder
660,118,300,365,430,394,366,301,428,392,119,299,117,367,429,393,121,303,368,426,390,122,304,369,427,391,120,302,370,425,389,298,116,371,436,400,296,114,372,434,398,297,115,373,435,399,112,294,374,432,396,113,295,375,433,397,431,111,293,376,395,668,671,661,664,438,156,104,402,454,102,154,403,452,439,155,437,103,401,453,441,159,100,405,450,442,157,101,406,451,440,158,99,404,449,162,444,110,408,460,160,445,108,409,458,161,443,109,407,459,447,165,106,411,456,448,163,107,412,457,410,446,164,105,455,685,687,688,686,268,340,541,478,502,539,338,476,500,266,339,267,540,477,501,264,336,537,474,498,265,337,538,475,499,263,335,536,473,497,331,259,547,484,508,329,257,545,482,506,330,258,546,483,507,262,334,543,480,504,260,332,544,481,505,479,261,333,542,503,669,662,666,665,12,173,585,586,529,582,174,581,527,13,172,14,584,583,528,11,176,577,578,525,9,177,579,580,526,10,175,575,576,524,171,3,597,598,535,169,4,594,593,533,170,5,595,596,534,6,167,589,590,531,7,168,591,592,532,587,8,166,588,530,683,676,679,682,517,185,556,418,192,554,186,416,190,515,184,516,555,417,191,513,188,552,414,195,514,189,553,415,193,512,187,551,413,194,183,523,562,424,198,181,521,560,422,196,182,522,561,423,197,519,179,558,420,201,520,180,559,421,199,419,518,178,557,200,670,667,672,663,315,28,490,382,328,488,29,380,326,316,30,314,489,381,327,311,31,486,378,324,312,32,487,379,325,313,33,485,377,323,26,306,496,388,319,27,307,494,386,317,25,305,495,387,318,309,22,492,384,322,310,23,493,385,320,383,308,24,491,321,698,697,693,694,632,49,634,635,633,626,45,627,625,624,47,628,630,631,629,510,41,548,600,2,511,44,549,601,1,509,40,550,599,0,37,657,658,659,656,38,649,650,651,648,39,653,654,655,652,641,36,642,643,640,645,34,646,647,644,639,637,35,638,636,703,701,702,704,222,48,207,212,125,205,50,213,126,223,46,221,206,214,124,225,15,203,211,128,226,42,204,209,129,224,43,202,210,127,17,228,622,218,623,18,229,618,219,619,16,227,620,220,621,231,20,614,217,615,232,21,617,215,616,216,230,19,208,123,699,696,700,695,568,356,290,466,607,291,357,464,605,566,358,567,292,465,606,564,355,289,462,603,565,353,287,463,604,563,354,288,461,602,362,574,281,472,613,363,572,282,470,611,364,573,283,471,612,570,361,284,468,609,571,359,285,469,610,467,569,360,286,608,674,681,684,675,247,96,146,239,138,147,97,240,136,245,98,246,145,241,137,250,95,142,242,141,248,93,143,243,139,249,94,144,244,140,87,253,152,237,133,88,251,153,238,134,89,252,151,236,135,256,90,148,233,132,254,91,149,234,130,235,255,92,150,131,678,677,680,673,57,78,347,64,277,348,79,65,275,58,80,59,349,63,276,60,77,350,67,280,61,75,351,68,278,62,76,352,66,279,84,55,345,70,272,85,56,346,71,273,86,54,344,69,274,51,83,341,73,271,52,81,342,74,269,72,53,82,343,270,690,691,689,692 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#ca58a4a9ddeee171fc40b5c556a5095e4a2c63eee13557dcdf190986f06d14c3. 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 18:16:17 · history