Equation 677 Database

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Magma 3905c5a252bf…

magma 3905c5a252bf
Size
381
Isomorphism class hash
3905c5a252bfa9104a254603cef17358b34f710b71467f1bf5e584bb6badd850
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 23:47:13
Display reorder
380,270,56,51,40,45,88,94,283,103,108,195,201,191,180,185,36,99,176,133,123,128,288,113,118,242,247,237,257,262,252,278,78,83,73,63,68,135,140,291,151,155,146,307,308,306,310,311,309,160,166,171,2,3,295,25,266,30,11,16,24,210,205,215,221,226,230,348,370,340,358,353,365,336,332,361,376,272,57,52,42,47,89,92,284,104,109,197,202,192,182,187,37,97,177,134,124,129,289,114,119,240,246,236,255,260,250,279,79,84,74,64,69,137,142,292,152,157,147,327,328,326,324,325,323,162,167,172,4,5,297,27,267,32,12,17,21,212,207,217,222,227,232,349,372,344,359,354,367,337,330,362,377,271,55,50,41,46,85,91,280,101,106,196,200,190,181,186,35,96,175,131,120,125,286,110,115,241,245,235,256,261,251,276,75,80,71,60,66,136,141,290,150,156,145,319,320,318,322,329,321,161,165,170,0,1,296,26,265,31,10,15,20,211,206,216,220,225,231,346,371,341,356,351,366,335,331,360,375,274,59,54,44,49,87,93,282,102,107,199,204,194,184,189,39,98,179,132,122,127,287,112,117,244,249,239,259,264,254,275,76,81,70,61,65,139,144,294,154,159,149,316,317,315,313,314,312,164,169,174,8,9,299,29,269,34,14,19,23,214,209,219,224,229,234,345,374,343,357,352,369,339,334,364,379,273,58,53,43,48,86,90,281,100,105,198,203,193,183,188,38,95,178,130,121,126,285,111,116,243,248,238,258,263,253,277,77,82,72,62,67,138,143,293,153,158,148,300,302,301,304,305,303,163,168,173,6,7,298,28,268,33,13,18,22,213,208,218,223,228,233,347,373,342,355,350,368,338,333,363,378 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#e1df87152eb4e0a2aee101822e1e35ad774d7a93b5a84f6ade065ecc70777444, M = {71} 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 23:47:14 · history