Equation 677 Database

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Magma b4db9287cf9d…

magma b4db9287cf9d
Size
381
Isomorphism class hash
b4db9287cf9d25b719a210eb656f26e784fa076779102fb2ce048bfb74244558
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 23:24:33
Display reorder
380,231,286,235,226,218,223,46,297,45,1,47,0,145,135,140,132,123,127,48,52,49,50,51,242,272,55,56,54,213,53,168,173,178,153,158,163,278,263,268,255,247,253,203,208,198,188,193,183,306,307,308,309,310,311,98,92,103,283,83,88,108,113,64,118,63,293,333,342,337,377,363,357,368,353,346,373,234,289,239,229,215,220,73,299,72,74,71,70,149,139,144,134,124,129,78,79,77,75,76,244,274,67,68,69,211,16,169,174,179,154,159,164,279,264,269,259,249,254,204,209,199,189,194,184,302,301,300,305,303,304,99,93,104,284,84,89,109,114,66,119,65,294,334,343,339,379,364,359,369,354,349,374,233,288,238,228,219,224,15,298,14,12,13,11,148,138,143,133,122,128,4,2,3,6,5,243,273,59,60,58,214,57,167,172,177,152,157,162,277,262,267,258,248,252,202,207,197,185,192,180,312,313,314,315,316,329,97,90,101,281,82,85,106,111,62,117,61,292,332,341,338,378,362,358,367,352,348,372,232,287,237,227,216,221,38,295,37,35,36,34,147,136,141,131,120,126,20,21,19,17,18,241,270,31,30,33,212,32,165,171,175,150,156,161,276,261,266,257,245,250,201,206,195,186,190,182,318,319,317,321,322,320,95,94,100,282,80,87,107,112,29,116,28,290,330,340,336,376,360,355,365,350,347,371,230,285,236,225,217,222,7,296,8,9,39,10,146,137,142,130,121,125,40,41,42,43,44,240,271,23,22,25,210,24,166,170,176,151,155,160,275,260,265,256,246,251,200,205,196,187,191,181,323,324,325,326,327,328,96,91,102,280,81,86,105,110,26,115,27,291,331,344,335,375,361,356,366,351,345,370 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 = {74} 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 23:24:34 · history