Equation 677 Database

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Magma 9f20bacf3a10…

magma 9f20bacf3a10
Size
381
Isomorphism class hash
9f20bacf3a104f7fdc7771b0937c0962bab76ccfa299a3b6b68301e7c91d7fc3
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 23:32:40
Display reorder
380,110,92,69,105,118,314,82,62,97,87,116,93,111,70,106,315,80,63,95,88,112,94,68,104,117,316,81,64,96,86,311,100,107,67,114,102,119,85,71,75,312,98,108,65,76,115,103,60,83,72,313,99,109,66,74,113,101,61,84,73,89,90,77,78,79,91,349,364,337,350,338,336,330,351,378,365,285,250,266,274,293,319,277,259,253,294,291,251,286,264,275,320,278,260,254,295,287,249,265,273,292,329,276,258,255,296,323,263,279,256,290,268,246,284,270,299,325,261,280,252,297,288,269,248,282,271,327,262,281,257,298,289,267,247,283,272,244,245,241,240,242,243,370,369,358,331,355,332,356,357,343,377,189,224,232,206,214,305,237,193,183,202,215,222,190,233,204,303,238,194,184,203,191,223,231,205,213,304,239,192,185,201,302,229,209,227,199,195,188,211,234,216,301,230,207,225,217,200,196,186,212,235,300,228,208,226,218,198,197,187,210,236,180,181,221,219,220,182,376,345,346,375,374,347,362,363,348,379,37,8,29,9,25,326,12,55,16,42,26,6,38,27,10,322,13,56,17,43,36,7,28,11,24,324,14,54,15,44,321,18,34,52,39,57,50,22,32,3,317,19,35,53,4,40,58,48,23,30,318,20,33,51,5,41,59,49,21,31,1,0,46,47,45,2,360,372,359,335,361,371,334,373,344,333,162,137,128,155,168,308,160,150,123,176,169,138,163,126,156,309,158,151,124,177,161,139,127,157,167,310,159,149,125,178,306,121,133,147,170,152,145,166,131,173,328,122,179,148,174,171,153,143,164,129,307,120,132,146,175,172,154,144,165,130,134,135,141,142,140,136,352,367,368,341,366,339,354,342,340,353 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#80df7fad9fa66fe51195cb8d2555ac1097b0db320b0a8ffa63e3cf8c589c8a0d, 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 23:32:41 · history