Equation 677 Database

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Magma 0b7cb4950750…

magma 0b7cb4950750
Size
381
Isomorphism class hash
0b7cb4950750a3c9018e2ff1faa6d1fc4339f9cb7944969e90ff0db7d3e4339e
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 23:49:05
Display reorder
380,177,202,182,187,192,197,157,162,167,172,147,152,267,272,277,252,257,262,117,122,127,132,137,142,67,72,77,82,57,62,107,112,87,92,97,102,303,304,305,301,300,302,292,22,23,24,25,282,217,32,287,297,207,212,247,227,232,242,237,222,28,29,30,31,26,27,350,331,367,349,364,359,341,378,371,340,178,203,183,189,194,199,159,164,169,173,148,153,268,273,278,254,259,263,118,123,128,134,138,143,69,74,79,84,58,64,108,114,88,93,98,103,328,329,324,325,326,327,294,39,34,36,38,284,218,54,289,299,209,213,248,229,234,244,239,224,51,42,44,46,48,50,352,344,365,346,361,356,332,377,372,342,175,201,180,185,190,195,155,160,165,171,145,150,266,271,275,251,256,261,116,121,126,130,135,140,65,70,75,80,56,61,106,110,86,91,96,101,312,313,314,315,316,317,291,13,14,0,2,281,215,1,285,295,205,210,246,226,231,241,236,220,19,20,15,16,17,18,351,334,369,347,360,355,337,376,370,339,179,204,184,188,193,198,158,163,168,174,149,154,269,274,279,253,258,264,119,124,129,133,139,144,68,73,78,83,59,63,109,113,89,94,99,104,323,318,319,320,321,322,293,40,33,35,37,283,219,53,288,298,208,214,249,228,233,243,238,223,52,41,43,45,47,49,353,343,368,345,362,357,338,379,373,335,176,200,181,186,191,196,156,161,166,170,146,151,265,270,276,250,255,260,115,120,125,131,136,141,66,71,76,81,55,60,105,111,85,90,95,100,308,309,310,311,306,307,290,9,10,11,12,280,216,21,286,296,206,211,245,225,230,240,235,221,6,7,8,3,4,5,354,330,366,348,363,358,336,375,374,333 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#e7d843eeb4140ee4f2ae7f87ad1590cd2b2e584cf01474530a75f9f611790378, M = {74} 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 23:49:07 · history