Equation 677 Database

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Magma afa76ba15e0d…

magma afa76ba15e0d
Size
381
Isomorphism class hash
afa76ba15e0dce2ec8d9fe5934eb15c2225b2491e0a929be6332ffc9488b7c12
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 23:26:24
Display reorder
380,78,77,79,75,290,76,83,84,85,80,81,82,233,238,243,248,253,228,325,326,327,328,329,324,72,73,74,69,70,71,64,289,65,66,67,68,188,193,198,203,177,183,148,153,158,163,168,173,61,62,63,58,59,60,115,298,218,223,208,213,258,283,263,268,273,278,333,344,363,337,367,348,357,352,372,378,53,57,54,55,288,56,30,31,32,33,34,35,232,237,242,247,252,227,321,322,317,318,319,320,47,48,49,50,51,52,45,287,46,42,43,44,187,190,195,200,176,182,147,152,157,162,167,172,38,39,40,41,36,37,86,297,217,222,207,212,257,282,262,267,272,277,331,343,362,335,365,347,356,351,371,377,9,22,0,2,286,21,24,25,26,27,28,23,230,235,241,246,251,225,304,301,300,323,302,303,3,4,5,6,7,8,20,285,16,17,18,19,186,191,196,201,178,181,146,150,155,160,165,170,15,10,11,12,13,14,1,295,215,220,206,210,255,281,261,266,271,276,336,341,361,339,369,345,355,354,370,376,96,95,97,93,291,94,101,102,103,98,99,100,231,236,240,245,250,226,316,311,312,313,314,315,90,91,92,87,88,89,114,292,110,111,112,113,185,192,197,202,175,180,145,151,156,161,166,171,109,104,105,106,107,108,29,296,216,221,205,211,256,280,260,265,270,275,334,342,360,338,373,346,350,358,366,375,125,124,126,122,293,123,130,131,132,127,128,129,234,239,244,249,254,229,307,308,309,310,305,306,119,120,121,116,117,118,143,294,139,140,141,142,189,194,199,204,179,184,149,154,159,164,169,174,138,133,134,135,136,137,144,299,219,224,209,214,259,284,264,269,274,279,330,340,364,332,374,349,353,359,368,379 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#51f9fa4941789fcec91b298b71630f6443ab313fec0bf96b206088496fe3251b, M = {66} 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 23:26:25 · history