Equation 677 Database

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Magma 5c9d40d6b90c…

magma 5c9d40d6b90c
Size
381
Isomorphism class hash
5c9d40d6b90cf92f08e0ae12cb14978c940db2e98f537ea39f3410fd75da8eeb
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 23:48:49
Display reorder
380,308,329,309,310,307,306,265,241,246,251,255,260,65,70,76,81,86,60,35,41,46,51,56,30,190,195,200,206,180,185,0,5,10,15,20,25,100,105,110,116,90,95,141,146,120,126,131,136,285,290,296,270,275,280,171,150,155,166,160,176,225,230,235,211,215,220,340,366,376,334,335,338,339,333,371,364,314,313,315,316,311,312,269,244,249,254,259,264,68,73,78,83,88,63,38,43,48,53,58,33,193,198,203,208,183,188,3,8,13,18,23,28,103,108,113,118,93,98,143,148,123,128,133,138,288,293,298,273,278,283,173,153,158,168,163,178,229,234,239,214,219,224,353,368,378,355,341,352,354,356,373,363,325,324,326,327,328,323,268,243,248,253,258,263,66,71,75,80,85,61,36,40,45,50,55,31,191,196,201,205,181,186,1,6,11,16,21,26,101,106,111,115,91,96,140,145,121,125,130,135,286,291,295,271,276,281,170,151,156,165,161,175,228,233,238,213,218,223,346,367,375,337,348,347,345,330,370,361,301,305,300,302,303,304,266,240,245,250,256,261,69,74,79,84,89,64,39,44,49,54,59,34,194,199,204,209,184,189,4,9,14,19,24,29,104,109,114,119,94,99,144,149,124,129,134,139,289,294,299,274,279,284,174,154,159,169,164,179,226,231,236,210,216,221,332,365,379,358,331,342,357,359,374,360,320,319,321,322,317,318,267,242,247,252,257,262,67,72,77,82,87,62,37,42,47,52,57,32,192,197,202,207,182,187,2,7,12,17,22,27,102,107,112,117,92,97,142,147,122,127,132,137,287,292,297,272,277,282,172,152,157,167,162,177,227,232,237,212,217,222,344,369,377,350,336,343,349,351,372,362 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 = {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 23:48:50 · history