Equation 677 Database

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Magma e71ee86aae65…

magma e71ee86aae65
Size
381
Isomorphism class hash
e71ee86aae654d8a386223323f57422537b512146d520228baf283394d5e86b3
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 23:24:09
Display reorder
380,159,154,164,169,174,179,224,214,219,239,229,234,199,204,209,184,189,194,19,299,18,144,149,139,324,325,326,327,328,329,49,54,59,64,69,279,6,7,287,97,102,107,29,33,24,274,44,39,72,282,77,82,87,92,254,249,244,264,269,259,129,134,119,124,114,294,339,334,363,344,369,352,359,347,374,379,155,150,160,166,171,176,221,211,216,235,225,230,196,201,205,180,185,190,3,296,2,141,146,136,311,309,310,308,306,307,46,51,56,60,65,276,8,9,288,98,103,108,28,32,23,270,40,36,73,283,78,83,88,93,253,248,243,263,268,258,126,130,115,121,110,291,335,333,361,341,365,353,356,348,371,376,157,152,162,167,172,177,222,212,217,237,227,232,197,202,207,182,187,192,13,297,12,142,147,137,305,303,304,302,301,300,45,50,55,61,66,275,4,5,285,96,101,106,25,34,20,271,41,35,71,280,76,80,85,90,250,246,241,260,265,255,127,132,117,122,112,292,336,330,362,340,367,350,357,345,372,377,156,151,161,165,170,175,220,210,215,236,226,231,195,200,206,181,186,191,11,295,10,140,145,135,318,319,320,321,322,323,47,52,57,62,67,277,1,0,286,95,100,105,27,30,22,272,42,37,70,281,75,81,86,91,252,247,242,262,267,257,125,131,116,120,111,290,337,332,360,342,366,351,355,346,370,375,158,153,163,168,173,178,223,213,218,238,228,233,198,203,208,183,188,193,17,298,16,143,148,138,312,313,314,315,316,317,48,53,58,63,68,278,14,15,289,99,104,109,26,31,21,273,43,38,74,284,79,84,89,94,251,245,240,261,266,256,128,133,118,123,113,293,338,331,364,343,368,354,358,349,373,378 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#4b20d49131fa1763d6463a102f127bf88ae35086a2437318b417535ceb91dad1, M = {68} 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 23:24:10 · history