Equation 677 Database

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Magma b56dff664be3…

magma b56dff664be3
Size
381
Isomorphism class hash
b56dff664be3fc0ff0b5ac7a3ad53b695bd24486824114b6c929209e55be0f61
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 23:23:38
Display reorder
380,54,272,55,213,52,53,133,123,128,148,138,143,61,62,63,64,244,65,83,86,91,283,73,78,163,153,158,178,168,173,56,60,57,58,59,299,228,219,223,288,233,238,308,306,307,311,309,310,268,278,263,253,258,248,103,98,293,113,118,108,188,193,208,183,203,198,353,363,343,359,373,348,333,368,338,378,33,270,34,211,0,1,130,120,125,145,136,141,9,10,8,12,240,11,81,88,92,280,71,76,161,151,156,175,165,170,35,39,36,37,38,297,225,216,220,286,231,236,312,313,329,315,316,314,266,276,261,250,255,245,101,96,290,110,116,105,185,190,205,181,200,195,350,360,340,357,371,346,330,365,336,376,15,271,14,210,31,32,131,121,126,146,135,140,26,27,28,29,242,30,80,87,93,281,70,75,160,150,155,176,166,171,19,25,18,16,17,296,226,217,221,285,230,235,318,319,317,321,322,320,265,275,260,251,256,246,100,95,291,111,115,106,186,191,206,180,201,196,351,361,341,356,370,345,331,366,335,375,7,273,6,212,40,41,132,122,127,147,137,142,47,48,49,50,243,51,82,85,90,282,72,77,162,152,157,177,167,172,42,46,43,44,45,298,227,218,222,287,232,237,303,304,305,301,300,302,267,277,262,252,257,247,102,97,292,112,117,107,187,192,207,182,202,197,352,362,342,358,372,347,332,367,337,377,68,274,69,214,66,67,134,124,129,149,139,144,4,5,3,2,241,13,84,89,94,284,74,79,164,154,159,179,169,174,20,21,22,23,24,295,229,215,224,289,234,239,324,325,323,327,328,326,269,279,264,254,259,249,104,99,294,114,119,109,189,194,209,184,204,199,354,364,344,355,374,349,334,369,339,379 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 = {66} 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 23:23:39 · history