Equation 677 Database

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Magma 3ac93816e492…

magma 3ac93816e492
Size
381
Isomorphism class hash
3ac93816e492ca8d7a1a5624c14a0e0c61405cacb550a0f1d21b8560e52cc15e
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 23:48:57
Display reorder
380,24,19,29,34,9,14,110,115,120,96,101,105,134,139,144,149,154,129,4,289,299,209,214,219,192,197,202,187,282,292,89,94,69,74,79,84,244,249,224,229,234,239,39,44,49,54,59,64,303,304,305,301,300,302,259,269,274,254,279,264,169,174,179,184,159,164,344,347,362,372,369,353,378,359,343,342,22,17,27,32,7,12,114,119,124,99,104,109,132,137,142,147,152,127,2,287,297,207,212,217,194,199,204,189,284,294,87,92,67,72,77,82,242,247,222,227,232,237,37,42,47,52,57,62,311,306,307,308,309,310,256,265,270,251,275,261,167,172,177,182,157,162,338,346,360,371,366,354,379,355,336,337,21,16,26,30,6,11,112,117,122,97,102,107,131,135,140,145,150,126,0,286,296,206,210,215,193,198,203,188,283,293,86,91,66,71,76,81,241,245,221,226,231,236,36,40,45,50,55,60,319,320,321,322,323,318,257,267,272,252,277,262,165,170,175,180,156,161,331,348,363,373,365,351,376,356,332,330,20,15,25,31,5,10,113,118,123,98,103,108,130,136,141,146,151,125,1,285,295,205,211,216,191,196,201,185,281,291,85,90,65,70,75,80,240,246,220,225,230,235,35,41,46,51,56,61,324,325,326,327,328,329,255,266,271,250,276,260,166,171,176,181,155,160,335,345,364,374,368,350,377,357,333,334,23,18,28,33,8,13,111,116,121,95,100,106,133,138,143,148,153,128,3,288,298,208,213,218,190,195,200,186,280,290,88,93,68,73,78,83,243,248,223,228,233,238,38,43,48,53,58,63,312,313,314,315,316,317,258,268,273,253,278,263,168,173,178,183,158,163,341,349,361,370,367,352,375,358,340,339 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 = {72} 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 23:48:58 · history