Equation 677 Database

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Magma 80b900ee2f7a…

magma 80b900ee2f7a
Size
381
Isomorphism class hash
80b900ee2f7a1ea2c274bff8b08e6af10d3d2500dc6c508ce30ff333fac32fa9
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 23:24:29
Display reorder
380,37,32,267,41,45,52,15,290,14,141,146,135,195,201,190,181,186,176,221,226,230,207,210,215,122,113,116,131,126,285,242,247,237,257,262,252,82,72,77,277,10,11,155,160,150,295,171,166,106,95,100,90,281,85,9,8,272,58,62,67,314,312,315,313,317,316,365,342,355,371,333,360,347,351,337,375,38,33,268,40,48,53,26,293,27,143,148,138,198,203,193,183,188,178,223,228,233,208,213,218,121,110,118,133,128,288,243,248,238,258,263,253,84,74,79,279,24,25,158,163,153,298,173,168,108,98,103,93,283,88,23,22,274,59,64,69,323,321,318,322,320,319,368,344,358,372,332,363,349,353,338,378,36,31,265,42,46,50,17,292,16,142,147,137,196,200,191,180,185,177,220,225,231,206,211,216,124,114,117,132,127,287,240,245,235,255,260,250,83,73,78,278,18,19,157,162,152,297,172,167,107,97,102,92,282,87,21,20,273,55,63,68,326,324,327,325,329,328,367,343,357,374,330,362,348,352,336,377,35,30,266,44,47,51,12,291,13,140,145,136,197,202,192,182,187,175,222,227,232,205,212,217,123,112,115,130,125,286,241,246,236,256,261,251,81,71,76,275,3,4,156,161,151,296,170,165,105,96,101,91,280,86,1,7,271,57,60,65,306,307,310,308,309,311,366,340,356,370,331,361,345,350,335,376,39,34,269,43,49,54,28,294,29,144,149,139,199,204,194,184,189,179,224,229,234,209,214,219,120,111,119,134,129,289,244,249,239,259,264,254,80,70,75,276,0,2,159,164,154,299,174,169,109,99,104,94,284,89,6,5,270,56,61,66,302,301,303,300,305,304,369,341,359,373,334,364,346,354,339,379 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#4b20d49131fa1763d6463a102f127bf88ae35086a2437318b417535ceb91dad1, M = {73} 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 23:24:30 · history