Equation 677 Database

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Magma d2c8f8375018…

magma d2c8f8375018
Size
381
Isomorphism class hash
d2c8f8375018c299056132fc5af4c27793a919a4e0a2e678ddf304ef9df64953
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 23:27:48
Display reorder
380,200,195,190,181,186,176,220,225,230,206,211,216,265,30,26,15,20,10,251,256,261,235,240,246,41,46,35,55,271,50,87,92,97,5,4,282,151,156,295,160,166,171,324,326,325,329,327,328,117,122,287,112,102,107,126,131,135,145,140,291,62,72,67,82,77,277,357,365,370,331,352,335,347,341,361,375,204,199,194,184,189,179,223,228,233,208,213,218,268,33,28,18,22,13,253,258,263,238,243,248,43,48,38,58,273,53,86,91,95,1,0,281,154,159,299,164,169,174,308,307,306,310,311,309,116,121,285,110,101,105,129,134,139,149,144,294,61,71,66,80,75,276,355,369,373,333,351,338,346,343,364,379,201,196,191,180,185,175,224,229,234,209,214,219,269,34,29,19,23,14,254,259,264,239,244,249,44,49,39,59,274,54,85,90,96,2,3,280,150,155,296,161,165,170,303,305,304,302,301,300,115,120,286,111,100,106,125,130,136,146,141,290,60,70,65,81,76,275,356,366,374,334,350,339,345,344,360,376,202,197,192,182,187,177,221,226,231,205,210,215,266,31,25,16,21,11,250,255,260,236,241,245,40,45,36,56,270,51,88,93,98,6,7,283,152,157,297,162,167,172,317,316,315,313,314,312,118,123,288,113,103,108,127,132,137,147,142,292,63,73,68,83,78,278,358,367,371,330,353,336,348,340,362,377,203,198,193,183,188,178,222,227,232,207,212,217,267,32,27,17,24,12,252,257,262,237,242,247,42,47,37,57,272,52,89,94,99,8,9,284,153,158,298,163,168,173,319,318,320,321,322,323,119,124,289,114,104,109,128,133,138,148,143,293,64,74,69,84,79,279,359,368,372,332,354,337,349,342,363,378 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#564914c332df918b1bab25ab6758cc0c591864f3f64c8c0ef251305010e22f83, M = {68} 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 23:27:49 · history