Equation 677 Database

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Magma e8a591318b0d…

magma e8a591318b0d
Size
595
Isomorphism class hash
e8a591318b0d6529873c1ffc0c480383d2ef00ed927942a90039e72f3f4afed7
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 594) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-08 13:15:27
Display reorder
51,53,52,50,48,49,113,112,111,108,109,110,87,89,88,86,84,85,321,320,322,323,318,319,445,444,446,447,448,449,522,514,526,565,575,152,154,153,157,155,156,140,139,138,141,142,143,176,175,174,177,178,179,147,148,170,145,146,144,187,195,191,183,256,253,198,200,199,197,196,249,237,239,238,241,242,240,30,32,31,34,35,33,453,452,454,455,450,451,337,336,338,339,340,341,265,264,266,267,268,269,426,431,427,428,429,430,435,434,436,437,432,433,475,474,476,477,478,479,317,316,312,313,314,315,381,380,382,383,378,379,537,511,534,544,531,539,543,551,572,577,590,560,593,559,556,578,204,206,205,203,201,202,232,231,233,236,234,235,250,254,180,193,185,189,76,75,77,74,72,73,91,90,92,93,94,95,2,0,1,4,5,3,133,132,134,137,135,136,221,220,219,222,223,224,460,459,461,456,457,458,281,280,276,277,278,279,471,470,472,473,468,469,504,509,505,506,507,508,411,410,412,413,408,409,325,324,326,327,328,329,356,355,357,358,359,354,285,284,286,287,282,283,518,548,545,533,550,540,523,530,587,586,591,557,563,581,573,584,126,128,127,131,129,130,165,164,166,169,167,168,57,59,58,55,56,54,6,8,7,10,11,9,67,66,68,69,70,71,100,99,101,96,97,98,28,27,29,26,24,25,115,114,116,119,117,118,403,402,404,405,406,407,464,463,465,466,467,462,502,501,503,498,499,500,351,350,352,353,348,349,485,484,480,481,482,483,289,288,290,291,292,293,263,262,259,258,260,261,304,303,305,300,301,302,510,527,529,524,536,515,517,520,594,589,562,567,569,585,568,554,214,213,215,216,217,218,227,226,225,228,229,230,252,257,181,194,186,190,63,65,64,61,62,60,78,80,79,83,81,82,47,46,45,43,44,42,124,123,125,122,120,121,150,149,151,171,172,173,395,394,390,391,392,393,419,418,414,415,416,417,369,368,370,371,366,367,493,492,494,495,496,497,344,343,345,346,347,342,309,308,310,311,306,307,424,423,425,420,421,422,387,386,388,389,384,385,516,538,546,513,549,541,521,528,592,579,564,555,570,580,558,576,21,23,22,20,18,19,14,13,12,15,16,17,158,160,159,162,163,161,107,106,105,102,103,104,184,192,188,182,255,251,244,243,245,246,247,248,209,208,207,210,211,212,41,40,39,36,37,38,296,295,297,298,299,294,400,399,401,396,397,398,491,490,486,487,488,489,270,275,271,272,273,274,335,334,330,331,332,333,443,442,438,439,440,441,373,372,374,375,376,377,363,362,364,365,360,361,525,512,519,552,532,535,542,547,553,566,582,583,571,574,561,588 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 595 = 35 + 5*112, 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#f04ca8125d7ce546c7552606527b36663a07f654279810fba8dfdb3271b338ee, M = the submagma generated by {24, 30} (35 elements) 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, 112): MacNeish's product over GF(16) x GF(7); GF(16) = F_2[x]/(x^4 + 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: 85.

last edited by qawbecrdtey at 2026-10-08 13:15:34 · history