Equation 677 Database

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Magma f9112d7de033…

magma f9112d7de033
Size
381
Isomorphism class hash
f9112d7de033a5749e2a0202e7ebb9fd8859749213436884eaee87a252ac97ab
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 23:23:42
Display reorder
380,170,180,175,166,155,161,1,0,2,3,291,4,313,314,312,316,317,315,191,196,185,205,210,200,215,36,41,56,46,51,7,220,6,66,71,61,226,90,95,86,75,80,101,106,230,111,116,120,135,125,132,150,140,146,296,286,281,270,275,266,255,260,246,250,241,236,350,365,335,330,340,355,345,375,370,364,173,183,178,168,158,163,21,22,23,24,293,25,324,325,326,327,328,329,193,198,188,208,213,203,218,38,43,58,48,53,27,223,26,68,73,63,228,93,98,88,78,83,103,108,233,113,118,123,137,128,133,153,143,148,298,288,283,273,278,268,258,263,248,253,243,238,353,368,338,332,343,358,348,378,373,362,172,182,177,167,156,162,17,18,16,20,292,19,307,308,306,310,311,309,192,197,187,207,212,202,217,37,42,57,47,52,14,222,15,67,72,62,227,92,97,87,77,82,102,107,232,112,117,122,139,127,131,152,142,147,297,287,282,272,277,267,257,262,247,252,242,237,352,367,337,333,342,357,347,377,372,360,174,184,179,169,159,164,31,32,30,34,294,33,304,305,303,300,302,301,194,199,189,209,214,204,219,39,44,59,49,54,28,224,29,69,74,64,229,94,99,89,79,84,104,109,234,114,119,124,138,129,134,154,144,149,299,289,284,274,279,269,259,264,249,254,244,239,354,369,339,334,344,359,349,379,374,363,171,181,176,165,157,160,10,11,9,13,290,12,318,319,320,321,322,323,190,195,186,206,211,201,216,35,40,55,45,50,5,221,8,65,70,60,225,91,96,85,76,81,100,105,231,110,115,121,136,126,130,151,141,145,295,285,280,271,276,265,256,261,245,251,240,235,351,366,336,331,341,356,346,376,371,361 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 = {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 23:23:43 · history