Equation 677 Database

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Magma ae2fcdb359d7…

magma ae2fcdb359d7
Size
381
Isomorphism class hash
ae2fcdb359d7b34c40590a0af46900d16c91ef9544b551d8f4d600e38b64e247
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 23:45:12
Display reorder
380,200,195,205,180,186,191,314,312,313,317,315,316,96,100,105,111,290,116,121,125,130,136,141,145,161,151,156,175,165,170,21,22,20,19,296,18,5,28,4,7,6,241,257,247,250,275,261,265,281,85,90,84,70,75,212,3,43,272,41,42,227,223,218,237,287,232,365,350,361,330,347,341,337,370,376,356,203,198,208,183,188,193,324,325,326,327,328,329,98,103,108,113,292,118,123,128,133,138,143,148,163,153,158,178,168,173,49,50,48,52,298,51,53,54,55,56,57,243,258,248,252,278,263,268,283,88,93,82,73,78,213,47,44,273,45,46,228,220,215,238,288,233,368,353,363,333,348,343,338,373,378,358,202,197,207,182,187,192,303,304,305,301,300,302,95,101,106,110,291,115,122,127,132,137,142,147,162,152,157,177,167,172,37,38,36,40,295,39,23,24,25,26,27,240,256,245,251,277,262,267,280,86,91,80,72,77,210,31,32,271,29,30,226,221,216,236,286,231,367,352,362,332,346,340,335,372,375,355,201,196,206,181,185,190,320,318,319,323,321,322,97,102,107,112,294,117,120,126,131,135,140,146,160,150,155,176,166,171,8,9,10,11,297,12,15,13,14,17,16,242,255,246,253,276,260,266,282,87,92,81,71,76,211,35,2,270,33,34,225,222,217,235,285,230,366,351,360,331,345,342,336,371,377,357,204,199,209,184,189,194,310,311,309,307,308,306,99,104,109,114,293,119,124,129,134,139,144,149,164,154,159,179,169,174,60,61,62,63,299,64,67,65,66,69,68,244,259,249,254,279,264,269,284,89,94,83,74,79,214,1,0,274,58,59,229,224,219,239,289,234,369,354,364,334,349,344,339,374,379,359 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#dba6afe67f86b36e533f777300b41b8ae8b2a840d4529c92a6cd7ab996e48d4f, 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 23:45:13 · history