Equation 677 Database

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Magma 3cc0f9de5815…

magma 3cc0f9de5815
Size
381
Isomorphism class hash
3cc0f9de5815fa41af5c445f0ca987f83a4790ae8ad7d2dcbf010a1f2ca7ccc1
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 23:48:13
Display reorder
380,316,315,317,312,313,314,177,167,172,162,152,157,38,37,41,297,39,40,43,44,42,242,46,45,117,112,292,107,97,102,87,92,84,77,282,72,232,237,287,217,222,227,122,127,132,137,142,147,197,202,207,181,185,192,49,48,50,51,272,212,261,275,265,257,247,252,366,347,337,332,357,342,362,352,372,376,328,327,329,324,325,326,176,166,171,161,150,155,27,25,26,295,28,29,0,2,3,241,36,47,116,111,290,106,96,101,85,90,82,76,280,70,230,235,286,216,221,226,120,125,130,135,140,145,196,200,205,183,187,190,19,18,20,17,271,210,260,276,266,255,246,250,367,346,335,330,355,340,361,350,370,377,304,303,305,301,300,302,175,165,170,160,151,156,4,5,6,296,1,30,33,31,32,240,34,35,115,110,291,105,95,100,86,91,80,75,281,71,231,236,285,215,220,225,121,126,131,136,141,146,195,201,206,182,188,191,22,21,23,24,270,211,262,277,267,256,245,251,365,345,336,331,356,341,360,351,371,375,318,320,319,323,321,322,178,168,173,163,153,158,15,16,14,298,13,12,11,9,10,243,7,8,118,113,293,108,98,103,88,93,81,78,283,73,233,238,288,218,223,228,123,128,133,138,143,148,198,203,208,184,189,193,53,52,54,55,273,213,263,278,268,258,248,253,368,348,338,334,358,343,363,353,373,378,309,311,310,308,306,307,179,169,174,164,154,159,64,56,57,299,62,63,67,68,69,244,65,66,119,114,294,109,99,104,89,94,83,79,284,74,234,239,289,219,224,229,124,129,134,139,144,149,199,204,209,180,186,194,59,58,60,61,274,214,264,279,269,259,249,254,369,349,339,333,359,344,364,354,374,379 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#e6667989dcd92e07f9ac29d8b243d6a96a38fa8a609415f393f811e1aaa26c76, 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 23:48:14 · history