Equation 677 Database

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Magma bf3a87f6cfd1…

magma bf3a87f6cfd1
Size
381
Isomorphism class hash
bf3a87f6cfd1315f9aa99851bdce11699c372ef2e26ef00c9995823f8d7fd682
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 23:24:17
Display reorder
380,26,21,31,35,210,41,171,176,166,157,162,152,243,248,238,258,263,253,13,14,12,233,293,15,115,226,110,101,106,95,322,320,321,319,317,318,205,196,200,191,183,188,66,56,61,53,45,216,126,133,121,141,147,137,70,80,75,91,86,220,275,266,281,270,296,286,341,345,351,358,361,330,365,374,335,378,28,24,34,38,213,43,174,179,169,159,164,154,244,249,239,259,264,254,17,18,16,234,294,19,118,228,113,103,108,98,323,324,325,326,327,328,209,199,204,194,181,186,69,59,64,50,48,218,129,132,124,144,149,139,74,84,79,93,88,223,279,269,284,274,299,289,343,348,353,359,364,334,369,373,338,379,29,22,32,39,214,44,170,175,165,155,160,150,241,246,235,255,261,250,4,5,3,230,291,6,119,229,114,104,109,99,305,303,304,302,301,300,207,197,202,192,184,189,65,55,60,52,49,219,127,130,122,142,146,136,71,81,76,94,89,224,277,267,282,272,297,287,344,349,354,355,360,331,367,371,339,376,27,23,33,37,212,42,173,178,168,158,163,153,240,245,236,256,260,251,7,0,1,231,290,2,117,227,112,102,107,97,308,306,307,311,309,310,208,198,203,193,180,185,68,58,63,51,47,217,128,134,123,143,148,138,73,83,78,92,87,222,278,268,283,273,298,288,342,347,352,356,363,333,368,372,337,375,25,20,30,36,211,40,172,177,167,156,161,151,242,247,237,257,262,252,10,8,9,232,292,11,116,225,111,100,105,96,329,312,313,316,314,315,206,195,201,190,182,187,67,57,62,54,46,215,125,131,120,140,145,135,72,82,77,90,85,221,276,265,280,271,295,285,340,346,350,357,362,332,366,370,336,377 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 = {70} 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 23:24:17 · history