Equation 677 Database

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Magma e02abc57e16e…

magma e02abc57e16e
Size
707
Isomorphism class hash
e02abc57e16e67b6cbd72a317269a24ee4a8a0668586c953d4b00fd8d30e6a0b
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 706) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-08 11:45:36
Display reorder
97,96,98,99,100,101,706,317,312,313,315,316,314,167,166,162,163,164,165,62,61,63,64,65,60,30,35,31,32,33,34,236,235,237,238,239,234,6,11,7,8,9,10,103,102,104,105,106,107,1,5,0,2,3,4,240,245,241,242,243,244,81,80,82,83,78,79,121,120,122,123,124,125,406,405,407,403,404,402,546,548,547,550,551,549,377,376,375,373,374,372,516,518,517,521,519,520,587,586,585,584,583,582,488,487,486,489,490,491,492,494,493,495,496,497,514,513,515,512,510,511,337,338,336,339,340,341,629,628,626,630,631,625,649,638,643,700,682,662,683,698,702,685,693,696,705,699,140,142,141,138,139,143,41,40,36,37,38,39,292,291,293,289,288,290,224,223,225,226,227,222,265,264,266,267,268,269,95,94,90,91,92,93,283,287,282,284,285,286,23,22,18,19,20,21,271,270,272,273,274,275,277,281,276,278,279,280,15,14,16,17,12,13,369,371,370,366,367,368,461,460,459,456,457,458,471,473,472,470,468,469,594,595,596,597,598,599,477,479,478,474,475,476,428,427,426,429,430,431,555,557,556,553,552,554,463,462,464,467,465,466,501,503,502,498,499,500,607,608,609,606,610,611,637,640,627,688,689,670,667,690,674,658,668,666,701,691,186,188,187,190,191,189,205,204,206,207,208,209,70,69,71,66,67,68,181,180,182,183,184,185,306,307,308,309,310,311,259,258,260,261,262,263,27,26,28,29,24,25,136,135,137,132,133,134,220,219,221,216,217,218,110,109,111,112,113,108,319,323,318,320,321,322,410,409,408,413,411,412,573,575,574,570,572,571,567,569,568,566,565,564,536,535,534,538,539,537,361,360,362,364,365,363,347,346,345,342,343,344,395,394,393,392,390,391,441,443,442,439,440,438,434,433,432,437,435,436,624,622,632,633,634,636,644,635,642,694,692,676,673,684,672,663,657,680,697,686,249,251,250,247,248,246,131,130,126,127,128,129,331,335,330,332,333,334,89,88,84,85,86,87,114,119,115,116,117,118,50,49,51,52,53,48,253,252,254,255,256,257,196,195,197,192,193,194,57,56,58,59,54,55,44,43,45,46,47,42,328,327,329,325,324,326,576,577,578,580,581,579,380,379,378,381,382,383,592,591,593,588,589,590,450,452,451,455,453,454,563,561,560,559,562,558,385,384,386,389,387,388,507,509,508,504,505,506,601,600,602,605,603,604,445,444,446,448,449,447,646,647,641,639,650,623,621,645,648,704,671,664,695,687,675,669,656,679,703,681,302,304,303,301,300,305,199,198,200,201,202,203,157,156,158,159,160,161,151,150,152,153,154,155,294,299,297,295,296,298,76,75,77,72,73,74,178,177,179,174,175,176,171,170,172,173,168,169,148,147,149,144,145,146,212,211,213,214,215,210,228,233,229,230,231,232,480,482,481,483,484,485,542,541,540,543,544,545,398,397,396,400,401,399,522,524,523,527,525,526,348,350,349,351,352,353,359,358,357,354,355,356,532,531,533,529,530,528,423,425,424,421,422,420,414,416,415,417,418,419,615,614,619,613,612,616,618,620,617,677,659,655,661,665,653,652,651,654,678,660 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 707 = 7 + 5*140, 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, 5, B) with E = magma#be842e4d65ca083f5f61a36963819b0aa7d50180968070250538ce7f22ff68d2, M = {60, 61, 62, 63, 64, 65, 145} in E, B = magma#e549b5f8492c9b6b5ad530e3aa4f39c6e23d08645ebd1b36a3c2de2a5a23bac5. 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(5, 140): MacNeish's product over GF(4) x GF(5) x GF(7); GF(4) = F_2[x]/(x^2 + 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: 101.

last edited by qawbecrdtey at 2026-10-08 11:45:38 · history