Equation 677 Database

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Magma 1d352be9548c…

magma 1d352be9548c
Size
381
Isomorphism class hash
1d352be9548c6636eaa17abda7160c198e61d6a0d92f81996de43cdb9c47aac3
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 23:47:41
Display reorder
380,143,293,148,138,128,133,151,156,295,165,170,161,114,104,109,124,119,289,319,320,318,322,323,321,200,191,196,185,176,180,226,231,221,211,216,206,42,47,37,57,272,52,84,74,79,69,279,64,284,8,9,99,89,94,240,236,245,251,256,261,266,10,15,24,26,32,336,342,330,354,359,371,362,365,375,349,142,292,147,137,127,132,153,158,298,168,173,163,113,103,108,123,118,288,301,300,302,303,304,305,203,193,198,188,178,183,228,233,222,213,218,208,43,48,38,58,273,53,83,73,78,68,278,63,283,6,7,98,88,93,244,239,249,254,259,264,268,13,18,22,28,33,338,343,334,353,358,373,364,368,378,348,140,290,146,135,125,130,150,155,296,166,171,160,110,102,105,122,117,287,313,314,312,316,317,315,201,190,195,186,175,181,225,230,220,210,215,205,40,45,35,56,271,51,82,72,77,67,277,62,282,4,5,97,87,92,242,237,247,252,258,263,265,11,16,20,25,31,335,341,332,352,357,370,360,366,376,347,144,294,149,139,129,134,154,159,299,169,174,164,111,101,106,121,115,286,308,306,307,311,309,310,204,194,199,189,179,184,229,234,224,214,219,209,44,49,39,59,274,54,81,70,75,66,275,61,280,2,3,95,85,90,241,235,246,250,257,262,269,14,19,23,29,34,339,344,331,350,356,374,363,369,379,345,141,291,145,136,126,131,152,157,297,167,172,162,112,100,107,120,116,285,324,325,326,327,328,329,202,192,197,187,177,182,227,232,223,212,217,207,41,46,36,55,270,50,80,71,76,65,276,60,281,1,0,96,86,91,243,238,248,253,255,260,267,12,17,21,27,30,337,340,333,351,355,372,361,367,377,346 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 = {76} 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 23:47:42 · history