Equation 677 Database

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Magma c7e4dea574c7…

magma c7e4dea574c7
Size
381
Isomorphism class hash
c7e4dea574c7142a5e49951e8f13d5abefc008d8617357e4d1f312d758870d08
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 23:23:49
Display reorder
380,243,59,60,61,62,63,113,118,108,65,293,64,134,124,129,149,139,144,273,213,52,53,14,13,154,159,164,169,174,179,268,278,263,253,258,248,184,189,194,199,204,209,57,298,58,54,55,56,218,223,228,233,238,288,306,308,307,311,309,310,98,103,88,94,80,283,358,364,338,368,353,334,343,347,378,374,241,5,6,3,35,4,112,117,107,51,292,50,133,123,128,148,138,143,271,210,1,21,19,20,153,158,163,168,173,178,265,275,260,252,256,247,182,187,192,197,202,207,28,295,27,25,26,24,215,221,226,231,236,286,316,315,317,312,313,314,96,102,87,91,83,282,355,363,335,366,352,332,342,349,376,373,242,48,47,16,49,15,111,116,106,18,291,17,130,120,125,145,136,141,270,211,22,23,12,11,151,156,161,165,170,175,267,277,262,251,257,246,181,186,191,195,200,205,46,297,45,43,44,42,216,220,225,230,235,285,304,303,305,301,300,302,95,100,86,90,82,280,357,360,336,367,351,330,340,346,377,371,244,74,73,77,75,76,114,119,109,79,294,78,131,121,126,146,135,140,274,214,69,67,68,66,150,155,160,166,171,176,269,279,264,254,259,249,180,185,190,196,201,206,71,299,70,0,72,2,219,224,229,234,239,289,323,322,321,319,320,318,99,104,89,93,84,284,359,361,339,369,354,331,344,348,379,370,240,34,33,31,32,30,110,115,105,37,290,36,132,122,127,147,137,142,272,212,41,39,40,38,152,157,162,167,172,177,266,276,261,250,255,245,183,188,193,198,203,208,29,296,7,9,10,8,217,222,227,232,237,287,327,329,328,326,324,325,97,101,85,92,81,281,356,362,337,365,350,333,341,345,375,372 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 = {67} 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 23:23:50 · history