Equation 677 Database

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Magma 076cb7ee8802…

magma 076cb7ee8802
Size
381
Isomorphism class hash
076cb7ee8802440e25caaa8658f480e9c3544bf7c3a0bdd7f30ab5b2e8761048
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 380) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-01 23:28:09
Display reorder
380,175,185,180,200,191,196,106,111,101,120,286,115,83,278,78,68,73,63,38,43,32,23,28,268,127,131,137,141,290,146,14,15,273,48,53,58,280,0,2,96,88,94,150,296,155,160,166,171,258,253,263,235,243,246,215,206,211,221,230,226,325,324,326,327,328,329,333,351,366,356,338,343,348,361,370,375,176,186,181,201,190,195,107,112,102,122,287,117,80,276,75,66,71,61,37,40,30,21,26,265,125,132,136,140,291,145,6,7,270,46,51,55,282,8,9,97,87,92,151,295,156,161,165,170,257,252,262,236,242,245,216,205,210,220,231,225,313,312,314,315,316,317,332,352,365,357,335,340,346,364,371,376,177,187,182,202,192,197,105,110,100,121,285,116,81,275,76,65,70,60,36,41,34,20,25,266,126,130,135,142,292,147,4,5,271,45,50,56,281,3,1,95,89,93,152,297,157,162,167,172,255,250,260,238,240,248,217,207,212,222,232,227,305,304,303,300,302,301,330,350,367,355,336,341,345,360,372,377,178,188,183,203,193,198,108,113,103,123,288,118,82,277,77,67,72,62,35,42,31,22,27,267,128,133,138,143,293,148,12,13,272,47,52,57,283,10,11,98,86,90,153,298,158,163,168,173,256,251,261,237,241,247,218,208,213,223,233,228,309,311,310,308,306,307,331,353,368,358,337,342,347,362,373,378,179,189,184,204,194,199,109,114,104,124,289,119,84,279,79,69,74,64,39,44,33,24,29,269,129,134,139,144,294,149,16,17,274,49,54,59,284,18,19,99,85,91,154,299,159,164,169,174,259,254,264,239,244,249,219,209,214,224,234,229,323,322,321,319,320,318,334,354,369,359,339,344,349,363,374,379 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 381 = 1 + 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#564914c332df918b1bab25ab6758cc0c591864f3f64c8c0ef251305010e22f83, M = {73} 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: 51.

last edited by qawbecrdtey at 2026-10-01 23:28:10 · history