Equation 677 Database

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Magma bf667f975e06…

magma bf667f975e06
Size
381
Isomorphism class hash
bf667f975e0654e1bf246bae1de562bdd96f1e690ae53579c22a41872938917c
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 23:42:54
Display reorder
380,265,261,256,245,250,240,182,186,192,195,200,205,115,120,291,101,106,110,37,27,32,277,42,47,236,226,231,220,212,215,160,152,155,176,166,171,295,126,131,146,135,141,2,7,272,16,22,12,324,325,326,327,328,329,70,65,60,50,57,282,75,80,286,95,86,91,342,337,351,356,345,330,375,360,366,372,269,264,259,249,254,244,184,189,194,199,204,209,119,124,294,104,109,114,39,29,34,279,44,49,239,229,234,224,214,219,164,154,159,179,169,174,299,129,134,149,139,144,4,9,274,18,24,14,312,313,314,315,316,317,74,69,64,54,59,284,79,84,289,99,89,94,344,339,354,359,348,334,379,364,369,374,268,263,258,248,253,242,183,188,193,198,203,207,117,122,292,102,107,112,35,26,30,275,41,46,238,228,233,223,213,218,163,153,158,178,168,173,297,127,132,147,137,142,1,6,270,15,20,10,306,307,308,309,310,311,71,67,61,52,55,281,77,82,287,97,87,92,340,335,352,357,346,332,377,362,367,373,267,262,257,247,252,241,180,187,191,196,201,206,118,123,293,103,108,113,36,25,31,276,40,45,237,227,232,222,210,217,161,151,156,175,165,170,298,128,133,148,138,143,0,5,271,19,21,11,318,319,320,321,322,323,73,68,63,53,58,283,78,83,288,98,88,93,341,336,353,358,347,331,376,363,365,370,266,260,255,246,251,243,181,185,190,197,202,208,116,121,290,100,105,111,38,28,33,278,43,48,235,225,230,221,211,216,162,150,157,177,167,172,296,125,130,145,136,140,3,8,273,17,23,13,300,302,301,304,305,303,72,66,62,51,56,280,76,81,285,96,85,90,343,338,350,355,349,333,378,361,368,371 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#c3f553b30d54716d9e2e87cb9ed350bbbf2e522a2867abba1f7ef649b9b0800a, M = {70} 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 23:42:54 · history