Equation 677 Database

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Magma 22571434e257…

magma 22571434e257
Size
595
Isomorphism class hash
22571434e2578749c7e97222b0e90daca3ee4b6699c8ca62c5576987f33678cc
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 10:31:21
Display reorder
270,271,272,273,274,275,351,350,352,353,348,349,507,506,508,509,505,504,340,339,341,336,337,338,344,343,345,346,347,342,530,593,591,594,592,75,74,76,72,73,71,84,83,85,88,86,87,117,116,118,115,113,114,120,119,121,124,122,123,287,286,285,283,284,282,81,80,82,77,78,79,111,110,112,108,109,107,91,90,89,92,93,94,98,100,99,95,96,97,106,105,104,101,102,103,367,366,368,369,370,371,365,364,360,361,362,363,384,389,385,386,387,388,381,380,382,383,378,379,485,484,480,481,482,483,374,373,375,376,377,372,535,551,536,514,527,517,548,537,524,560,561,588,580,573,568,583,3,5,4,1,0,2,159,158,160,157,155,156,181,180,179,182,183,184,190,189,188,185,186,187,290,289,288,292,293,291,239,241,240,244,242,243,175,174,173,178,176,177,166,165,164,161,162,163,167,169,168,170,171,172,265,266,264,268,269,267,470,469,471,472,473,468,462,467,463,464,465,466,431,430,426,427,428,429,422,421,423,424,425,420,494,493,495,496,497,492,419,418,414,415,416,417,531,553,539,513,525,516,547,540,523,558,563,586,579,572,567,582,152,154,153,149,150,151,251,7,6,8,9,10,11,13,12,15,16,14,20,22,21,17,19,18,300,302,301,305,303,304,148,147,146,144,145,143,141,140,142,138,139,137,255,257,256,253,254,252,128,130,129,125,126,127,136,135,134,131,132,133,405,404,406,407,402,403,411,410,412,413,408,409,313,312,314,315,316,317,308,306,309,310,311,307,490,489,491,486,487,488,397,396,398,399,400,401,538,555,544,511,528,519,550,532,520,557,565,590,576,575,569,584,247,245,246,250,248,249,202,201,200,197,198,199,229,228,227,230,231,232,238,237,236,233,234,235,294,296,295,299,297,298,193,192,191,195,196,194,223,222,221,226,224,225,206,208,207,204,205,203,210,209,211,213,214,212,215,217,216,219,220,218,438,443,439,440,441,442,436,435,437,432,433,434,461,460,456,457,458,459,452,451,453,454,455,450,502,501,503,498,499,500,445,444,446,447,448,449,542,554,545,510,529,518,549,541,521,556,564,589,577,574,570,585,24,23,25,27,28,26,48,47,49,52,50,51,40,39,38,35,36,37,31,30,29,32,33,34,279,281,280,278,277,276,42,41,43,44,45,46,66,65,67,69,70,68,53,55,54,57,58,56,61,60,59,64,62,63,260,258,259,261,262,263,320,319,321,322,323,318,394,393,395,390,391,392,332,331,333,334,335,330,329,328,324,325,326,327,479,478,475,474,476,477,358,357,359,354,355,356,533,552,534,512,526,515,546,543,522,559,562,587,578,571,566,581 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#54e3a19f93137e404c924a9b37966faa8299b270c95916aef4ed0fa8730aa82d, M = the submagma generated by {42, 66} (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 10:31:22 · history