Equation 677 Database

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Magma 7ded1a0b9b0e…

magma 7ded1a0b9b0e
Size
381
Isomorphism class hash
7ded1a0b9b0ed2799c20a31cdda4c444b1c8847a50a0ef7bed581107c53cb99d
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 23:24:41
Display reorder
380,318,117,100,85,110,60,68,75,91,103,319,69,86,111,61,76,92,104,101,118,314,87,112,62,96,77,119,105,70,93,315,88,113,63,71,97,72,94,114,106,89,316,108,64,66,98,73,95,115,107,317,84,109,65,67,99,74,90,116,102,83,79,80,81,82,78,350,375,347,348,379,378,366,346,365,349,323,147,130,179,140,154,156,163,121,133,325,157,174,141,155,164,122,134,131,148,327,175,142,150,126,165,149,135,158,123,329,176,143,151,159,127,166,124,144,136,177,301,138,152,160,128,167,125,145,137,321,178,139,153,161,129,162,120,146,132,171,173,168,169,170,172,353,333,330,367,332,351,354,331,368,352,304,210,193,184,209,217,225,232,190,202,305,226,185,204,218,233,191,203,194,211,306,180,205,219,195,228,212,198,227,186,307,181,206,220,222,196,229,187,213,199,182,302,207,221,223,197,230,188,214,200,303,183,208,216,224,192,231,189,215,201,234,236,237,238,239,235,377,370,335,334,355,369,356,336,337,376,313,240,287,272,297,247,255,262,278,290,308,256,273,298,248,263,279,291,282,241,309,274,299,249,283,258,242,292,257,280,310,275,294,250,252,284,259,281,243,293,270,311,295,251,253,285,260,276,244,288,312,271,296,246,254,286,261,277,245,289,264,266,267,268,269,265,339,358,360,371,372,361,362,359,357,338,300,17,58,43,10,18,26,33,49,3,320,27,44,11,19,34,50,4,59,12,322,45,6,20,54,35,13,5,28,51,324,46,7,21,29,55,30,52,14,1,47,326,8,22,24,56,31,53,15,0,328,42,9,23,25,57,32,48,16,2,41,37,38,39,40,36,373,343,374,363,341,345,340,344,342,364 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#4c97df0f82d8083b5ed30a31fc43835927c9c01ead672ecaafd0d0259928da19, 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 23:24:42 · history