Equation 677 Database

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Magma 0a8c604ecdf3…

magma 0a8c604ecdf3
Size
399
Isomorphism class hash
0a8c604ecdf33565b71e9a9d5da050d5bf9877d1718a05da27f8ee94cf99278c
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 398) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-06 21:28:50
Display reorder
310,311,312,313,314,306,307,308,309,319,320,321,322,323,315,316,317,318,378,130,275,302,327,131,328,276,303,132,329,277,304,133,330,278,305,134,331,270,297,126,332,271,298,127,324,272,299,128,325,273,300,129,326,274,301,284,336,139,295,285,337,140,296,141,286,338,288,287,339,142,289,279,340,143,290,280,341,135,291,281,333,136,292,282,334,137,293,283,335,138,294,391,385,386,392,185,237,258,58,186,59,238,259,187,60,239,260,188,61,240,252,180,62,241,253,181,54,242,254,182,55,234,255,183,56,235,256,184,57,236,257,246,67,194,267,247,68,195,268,196,248,69,269,249,70,197,261,250,71,189,262,251,63,190,263,243,64,191,264,244,65,192,265,245,66,193,266,383,389,390,384,37,35,201,73,38,74,27,202,39,75,28,203,40,76,29,204,41,77,30,205,42,78,31,206,43,79,32,198,44,80,33,199,36,72,34,200,19,82,46,210,20,83,47,211,48,21,84,212,22,85,49,213,23,86,50,214,24,87,51,215,25,88,52,207,26,89,53,208,18,81,45,209,388,398,397,387,114,169,342,349,115,351,170,344,116,353,162,346,108,354,163,348,109,356,164,350,110,358,165,352,111,343,166,355,112,345,167,357,113,347,168,359,178,367,123,360,179,369,124,362,125,171,371,364,172,372,117,366,173,374,118,368,174,376,119,370,175,361,120,373,176,363,121,375,177,365,122,377,394,395,396,393,91,16,217,153,92,154,17,218,93,155,9,219,94,156,10,220,95,157,11,221,96,158,12,222,97,159,13,223,98,160,14,224,90,161,15,216,1,146,100,226,0,147,101,227,102,2,148,228,3,149,103,229,4,150,104,230,5,151,105,231,6,152,106,232,7,144,107,233,8,145,99,225,382,380,379,381 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 399 = 19 + 5*76, 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#c0a5ff49ef7673e13fb8ee7daad83e6a56a7bbecbc291728281cccc30594a3ad, M = the submagma generated by {0} (19 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, 76): MacNeish's product over GF(4) x GF(19); 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: 21.

last edited by qawbecrdtey at 2026-10-06 21:28:51 · history